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Mathematics of particle-wave mechanical systems / / James M. Hill
| Mathematics of particle-wave mechanical systems / / James M. Hill |
| Autore | Hill James M. |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (388 pages) |
| Disciplina | 530.15 |
| Soggetto topico |
Mathematical physics
Special relativity (Physics) Física matemàtica Relativitat especial (Física) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031197932
9783031197925 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Author's Foreword -- Contents -- 1 Introduction -- 1.1 Introduction -- 1.2 General Introduction -- 1.3 Special Relativity -- 1.4 Quantum Mechanics -- 1.5 de Broglie Particle-Wave Mechanics -- 1.6 Plan of Text -- 1.7 Tables of Major Symbols and Basic Equations -- 2 Special Relativity -- 2.1 Introduction -- 2.2 Lorentz Transformations -- 2.3 Einstein Addition of Velocities Law -- 2.4 Lorentz Invariances -- 2.5 Lorentz Invariant Velocity Fields u(x, t) -- 2.6 General Framework for Lorentz Invariances -- 2.7 Integral Invariants of the Lorentz Group -- 2.8 Alternative Validation of Lorentz Invariants -- 2.9 Jacobians of the Lorentz Transformations -- 2.10 Space-Time Transformation x'= ct and t' = x/c -- 2.11 The de Broglie Wave Velocity u'= c2/u -- 2.12 Force and Physical Energy Arising from Work Done -- 2.13 Lorentz Invariant Energy-Momentum Relations -- 2.14 Force Invariance for Constant Velocity Frames -- 2.15 Example: Motion in an Invariant Potential Field -- 2.16 Alternative Energy-Mass Velocity Variation -- 3 General Formulation and Basic Equations -- 3.1 Introduction -- 3.2 Louis Victor de Broglie -- 3.3 James Clerk Maxwell -- 3.4 Four Types of Matter and Variable Rest Mass -- 3.5 Modified Newton's Laws of Motion -- 3.6 Identity for Spatial Physical Force ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (bold f) /StPNE pdfmark [/StBMC pdfmarkfps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 3.7 Assumed Existence of Work Done Function ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (upper W left parenthesis bold x comma t right parenthesis) /StPNE pdfmark [/StBMC pdfmarkW(x, t)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark.
3.8 Forces ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (bold f) /StPNE pdfmark [/StBMC pdfmarkfps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and g Derivable from a Potential ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (upper V left parenthesis bold x comma t right parenthesis) /StPNE pdfmark [/StBMC pdfmarkV(x, t)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 3.9 Correspondence with Maxwell's Equations -- 3.10 Centrally or Spherically Symmetric Systems -- 3.11 Newtonian Kinetic Energy and Momentum -- 3.12 Newtonian Wave-Like Solution -- 3.13 Newtonian Work Done ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (upper W left parenthesis u comma lamda right parenthesis) /StPNE pdfmark [/StBMC pdfmarkW(u, λ)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark from ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (partial differential f divided by partial differential t equals c squared partial differential g divided by partial differential x) /StPNE pdfmark [/StBMC pdfmark∂f/∂t = c2 ∂g/∂xps: [/EMC pdfmark [/StPop pdf -- 4 Special Results for One Space Dimension -- 4.1 Introduction -- 4.2 Basic Equations -- 4.3 General Reformulations of Basic Equations -- 4.4 Important Identity -- 4.5 Formulation in Terms of Lorentz Invariants -- 4.6 Differential Relations for Invariants ξ and η -- 4.7 de Broglie's Guidance Equation -- 4.8 Vanishing of Force g in Direction of Time -- 4.9 Clairaut's Differential Equation with Parameter u -- 4.10 Hamiltonian for One Space Dimension -- 4.11 Lagrangian for One Space Dimension -- 5 Exact Wave-Like Solution -- 5.1 Introduction -- 5.2 Wave-Like Solution -- 5.3 Work Done W(u, λ) from ∂f/∂t = c2 ∂g/∂x -- 5.4 Simple Derivation of Wave-Like Solution -- 5.5 Relation to Solution of Special Relativity -- 5.6 Relation to Hubble Parameter. 5.7 Derivation of Integral for Hubble Formula -- 5.8 Dark Matter and Dark Energy as de Broglie States -- 6 Derivations and Formulae -- 6.1 Introduction -- 6.2 Derivation of Wave-Like Solution -- 6.3 Expressions for de Broglie Wave Energy -- 6.4 de Broglie Wave Energy for Particular λ -- 6.5 Alternative Approach to Evaluation of Integrals -- 6.6 Alternative Derivation for Wave Energy -- 6.7 Alternative Derivation of Exact Solution -- 6.8 Yet Another Approach to Evaluation of Integrals -- 7 Lorentz and Other Invariances -- 7.1 Introduction -- 7.2 Force Invariance Under Lorentz Transformations -- 7.3 Lorentz Invariance of ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (d script upper E divided by d p) /StPNE pdfmark [/StBMC pdfmarkd E/dpps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark or ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (d script upper E divided by d xi) /StPNE pdfmark [/StBMC pdfmarkdE/dξps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 7.4 Lorentz Invariance of Forces -- 7.5 Functional Dependence of Forces -- 7.6 Transformation x'= ct and t' = x/c -- 7.7 Force Invariance Under Superluminal Lorentz Frames -- 7.8 Particle and Wave Energies and Momenta -- 8 Further Results for One Space Dimension -- 8.1 Introduction -- 8.2 Wave Equation General Solution -- 8.3 Trivial Solution Only for Zero Spatial Force -- 8.4 Nontrivial Solutions for Zero Spatial Force -- 8.5 Generalisation of Wave-Like Solution -- 8.6 Solutions with Non-constant Rest Mass -- 8.7 Formulation for Variable Rest Mass. 8.8 Characteristics ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (alpha equals c t plus x) /StPNE pdfmark [/StBMC pdfmarkα= ct + xps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (beta equals c t minus x) /StPNE pdfmark [/StBMC pdfmarkβ= ct - xps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 8.9 p(x, t) and ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (script upper E left parenthesis x comma t right parenthesis) /StPNE pdfmark [/StBMC pdfmarkE(x, t)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark Assumed Independent Variables -- 9 Centrally Symmetric Mechanical Systems -- 9.1 Introduction -- 9.2 Basic Equations with Spherical Symmetry -- 9.3 General Solutions for ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (script upper E left parenthesis r comma t right parenthesis) /StPNE pdfmark [/StBMC pdfmarkE(r, t)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and p(r, t) -- 9.4 Conservation of Energy ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (e plus script upper E plus upper V equals) /StPNE pdfmark [/StBMC pdfmarke + E + V = ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark Constant -- 9.5 Fundamental Identity for f and g -- 9.6 ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (f equals plus or minus c left parenthesis g minus 2 p divided by r right parenthesis) /StPNE pdfmark [/StBMC pdfmarkf = c(g -2p/r)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark Implies e0 Is Zero -- 9.7 Newtonian Gravitation and Schwarzschild Radius -- 9.8 Pseudo-Newtonian Gravitational Potential -- 9.9 Dark Matter-Dark Energy and Four Types of Matter. 9.10 Positive Energy (I) e = (e02 + (pc)2)1/2, ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (e 0 not equals 0) /StPNE pdfmark [/StBMC pdfmarke0 ≠0ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 9.11 Negative Energy (II) e = - (e02 + (pc)2)1/2, ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (e 0 not equals 0) /StPNE pdfmark [/StBMC pdfmarke0≠0ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 9.12 Positive Energy (III) e = pc, e0 = 0 -- 9.13 Negative Energy (IV) e = -pc, e0 = 0 -- 9.14 Similarity Stretching Solutions of Wave Equation -- 9.15 Some Examples Involving the Dirac Delta Function -- 9.16 Calculation Details for Similarity Solutions -- 9.17 de Broglie's Centrally Symmetric Guidance Formula -- 10 Relation with Quantum Mechanics -- 10.1 Introduction -- 10.2 Quantum Mechanics and Schrödinger Wave Equation -- 10.3 Group Velocity and de Broglie Waves -- 10.4 Lorentz Invariants ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (xi equals e x minus c squared p t) /StPNE pdfmark [/StBMC pdfmarkξ= ex - c2 ptps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (eta equals p x minus e t) /StPNE pdfmark [/StBMC pdfmarkη= px - etps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 10.5 Klein-Gordon Partial Differential Equation -- 10.6 Alternative Klein-Gordon-Schrödinger Equation -- 10.7 General Wave Structure of Solutions of Wave Equation -- 10.8 Wave Solutions of Klein-Gordon Equation -- 10.9 Time-Dependent Dirac Equation for Free Particle -- 11 Coordinate Transformations, Tensors and General Relativity -- 11.1 Summation Convention and Cartesian Tensors -- 11.2 Alternative Derivation of Basic Identity -- 11.3 General Curvilinear Coordinates -- 11.4 Partial Covariant Differentiation -- 11.5 Illustration for Single Space Dimension. 11.6 Formulae for Ricci and Einstein Tensors. |
| Record Nr. | UNINA-9910633911203321 |
Hill James M.
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Mathematics of particle-wave mechanical systems / / James M. Hill
| Mathematics of particle-wave mechanical systems / / James M. Hill |
| Autore | Hill James M. |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (388 pages) |
| Disciplina | 530.15 |
| Soggetto topico |
Mathematical physics
Special relativity (Physics) Física matemàtica Relativitat especial (Física) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783031197932
9783031197925 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Author's Foreword -- Contents -- 1 Introduction -- 1.1 Introduction -- 1.2 General Introduction -- 1.3 Special Relativity -- 1.4 Quantum Mechanics -- 1.5 de Broglie Particle-Wave Mechanics -- 1.6 Plan of Text -- 1.7 Tables of Major Symbols and Basic Equations -- 2 Special Relativity -- 2.1 Introduction -- 2.2 Lorentz Transformations -- 2.3 Einstein Addition of Velocities Law -- 2.4 Lorentz Invariances -- 2.5 Lorentz Invariant Velocity Fields u(x, t) -- 2.6 General Framework for Lorentz Invariances -- 2.7 Integral Invariants of the Lorentz Group -- 2.8 Alternative Validation of Lorentz Invariants -- 2.9 Jacobians of the Lorentz Transformations -- 2.10 Space-Time Transformation x'= ct and t' = x/c -- 2.11 The de Broglie Wave Velocity u'= c2/u -- 2.12 Force and Physical Energy Arising from Work Done -- 2.13 Lorentz Invariant Energy-Momentum Relations -- 2.14 Force Invariance for Constant Velocity Frames -- 2.15 Example: Motion in an Invariant Potential Field -- 2.16 Alternative Energy-Mass Velocity Variation -- 3 General Formulation and Basic Equations -- 3.1 Introduction -- 3.2 Louis Victor de Broglie -- 3.3 James Clerk Maxwell -- 3.4 Four Types of Matter and Variable Rest Mass -- 3.5 Modified Newton's Laws of Motion -- 3.6 Identity for Spatial Physical Force ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (bold f) /StPNE pdfmark [/StBMC pdfmarkfps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 3.7 Assumed Existence of Work Done Function ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (upper W left parenthesis bold x comma t right parenthesis) /StPNE pdfmark [/StBMC pdfmarkW(x, t)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark.
3.8 Forces ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (bold f) /StPNE pdfmark [/StBMC pdfmarkfps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and g Derivable from a Potential ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (upper V left parenthesis bold x comma t right parenthesis) /StPNE pdfmark [/StBMC pdfmarkV(x, t)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 3.9 Correspondence with Maxwell's Equations -- 3.10 Centrally or Spherically Symmetric Systems -- 3.11 Newtonian Kinetic Energy and Momentum -- 3.12 Newtonian Wave-Like Solution -- 3.13 Newtonian Work Done ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (upper W left parenthesis u comma lamda right parenthesis) /StPNE pdfmark [/StBMC pdfmarkW(u, λ)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark from ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (partial differential f divided by partial differential t equals c squared partial differential g divided by partial differential x) /StPNE pdfmark [/StBMC pdfmark∂f/∂t = c2 ∂g/∂xps: [/EMC pdfmark [/StPop pdf -- 4 Special Results for One Space Dimension -- 4.1 Introduction -- 4.2 Basic Equations -- 4.3 General Reformulations of Basic Equations -- 4.4 Important Identity -- 4.5 Formulation in Terms of Lorentz Invariants -- 4.6 Differential Relations for Invariants ξ and η -- 4.7 de Broglie's Guidance Equation -- 4.8 Vanishing of Force g in Direction of Time -- 4.9 Clairaut's Differential Equation with Parameter u -- 4.10 Hamiltonian for One Space Dimension -- 4.11 Lagrangian for One Space Dimension -- 5 Exact Wave-Like Solution -- 5.1 Introduction -- 5.2 Wave-Like Solution -- 5.3 Work Done W(u, λ) from ∂f/∂t = c2 ∂g/∂x -- 5.4 Simple Derivation of Wave-Like Solution -- 5.5 Relation to Solution of Special Relativity -- 5.6 Relation to Hubble Parameter. 5.7 Derivation of Integral for Hubble Formula -- 5.8 Dark Matter and Dark Energy as de Broglie States -- 6 Derivations and Formulae -- 6.1 Introduction -- 6.2 Derivation of Wave-Like Solution -- 6.3 Expressions for de Broglie Wave Energy -- 6.4 de Broglie Wave Energy for Particular λ -- 6.5 Alternative Approach to Evaluation of Integrals -- 6.6 Alternative Derivation for Wave Energy -- 6.7 Alternative Derivation of Exact Solution -- 6.8 Yet Another Approach to Evaluation of Integrals -- 7 Lorentz and Other Invariances -- 7.1 Introduction -- 7.2 Force Invariance Under Lorentz Transformations -- 7.3 Lorentz Invariance of ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (d script upper E divided by d p) /StPNE pdfmark [/StBMC pdfmarkd E/dpps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark or ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (d script upper E divided by d xi) /StPNE pdfmark [/StBMC pdfmarkdE/dξps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 7.4 Lorentz Invariance of Forces -- 7.5 Functional Dependence of Forces -- 7.6 Transformation x'= ct and t' = x/c -- 7.7 Force Invariance Under Superluminal Lorentz Frames -- 7.8 Particle and Wave Energies and Momenta -- 8 Further Results for One Space Dimension -- 8.1 Introduction -- 8.2 Wave Equation General Solution -- 8.3 Trivial Solution Only for Zero Spatial Force -- 8.4 Nontrivial Solutions for Zero Spatial Force -- 8.5 Generalisation of Wave-Like Solution -- 8.6 Solutions with Non-constant Rest Mass -- 8.7 Formulation for Variable Rest Mass. 8.8 Characteristics ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (alpha equals c t plus x) /StPNE pdfmark [/StBMC pdfmarkα= ct + xps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (beta equals c t minus x) /StPNE pdfmark [/StBMC pdfmarkβ= ct - xps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 8.9 p(x, t) and ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (script upper E left parenthesis x comma t right parenthesis) /StPNE pdfmark [/StBMC pdfmarkE(x, t)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark Assumed Independent Variables -- 9 Centrally Symmetric Mechanical Systems -- 9.1 Introduction -- 9.2 Basic Equations with Spherical Symmetry -- 9.3 General Solutions for ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (script upper E left parenthesis r comma t right parenthesis) /StPNE pdfmark [/StBMC pdfmarkE(r, t)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and p(r, t) -- 9.4 Conservation of Energy ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (e plus script upper E plus upper V equals) /StPNE pdfmark [/StBMC pdfmarke + E + V = ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark Constant -- 9.5 Fundamental Identity for f and g -- 9.6 ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (f equals plus or minus c left parenthesis g minus 2 p divided by r right parenthesis) /StPNE pdfmark [/StBMC pdfmarkf = c(g -2p/r)ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark Implies e0 Is Zero -- 9.7 Newtonian Gravitation and Schwarzschild Radius -- 9.8 Pseudo-Newtonian Gravitational Potential -- 9.9 Dark Matter-Dark Energy and Four Types of Matter. 9.10 Positive Energy (I) e = (e02 + (pc)2)1/2, ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (e 0 not equals 0) /StPNE pdfmark [/StBMC pdfmarke0 ≠0ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 9.11 Negative Energy (II) e = - (e02 + (pc)2)1/2, ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (e 0 not equals 0) /StPNE pdfmark [/StBMC pdfmarke0≠0ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 9.12 Positive Energy (III) e = pc, e0 = 0 -- 9.13 Negative Energy (IV) e = -pc, e0 = 0 -- 9.14 Similarity Stretching Solutions of Wave Equation -- 9.15 Some Examples Involving the Dirac Delta Function -- 9.16 Calculation Details for Similarity Solutions -- 9.17 de Broglie's Centrally Symmetric Guidance Formula -- 10 Relation with Quantum Mechanics -- 10.1 Introduction -- 10.2 Quantum Mechanics and Schrödinger Wave Equation -- 10.3 Group Velocity and de Broglie Waves -- 10.4 Lorentz Invariants ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (xi equals e x minus c squared p t) /StPNE pdfmark [/StBMC pdfmarkξ= ex - c2 ptps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and ps: [/EMC pdfmark [/objdef Equ /Subtype /Span /ActualText (eta equals p x minus e t) /StPNE pdfmark [/StBMC pdfmarkη= px - etps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 10.5 Klein-Gordon Partial Differential Equation -- 10.6 Alternative Klein-Gordon-Schrödinger Equation -- 10.7 General Wave Structure of Solutions of Wave Equation -- 10.8 Wave Solutions of Klein-Gordon Equation -- 10.9 Time-Dependent Dirac Equation for Free Particle -- 11 Coordinate Transformations, Tensors and General Relativity -- 11.1 Summation Convention and Cartesian Tensors -- 11.2 Alternative Derivation of Basic Identity -- 11.3 General Curvilinear Coordinates -- 11.4 Partial Covariant Differentiation -- 11.5 Illustration for Single Space Dimension. 11.6 Formulae for Ricci and Einstein Tensors. |
| Record Nr. | UNISA-996499865703316 |
|
Hill James M.
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Special Relativity : An Introduction with 200 Problems and Solutions / / by Michael Tsamparlis
| Special Relativity : An Introduction with 200 Problems and Solutions / / by Michael Tsamparlis |
| Autore | Tsamparlis Michael |
| Edizione | [2nd ed. 2019.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 |
| Descrizione fisica | 1 online resource (xxv, 815 pages) : illustrations (some color) |
| Disciplina | 530.11 |
| Collana | Undergraduate Lecture Notes in Physics |
| Soggetto topico |
Gravitation
Cosmology Mathematical physics Classical and Quantum Gravity Mathematical Physics Relativitat especial (Física) Física matemàtica Educació superior |
| Soggetto genere / forma |
Problemes i exercicis
Llibres electrònics |
| ISBN | 3-030-27347-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Mathematical Part -- The Structure of the Theories of Physics -- Newtonian Physics -- The Foundation of Special Relativity -- The Physics of the Position Four-Vector -- Relativistic Kinematics -- Four-Acceleration -- Paradoxes -- Mass – Four-Momentum -- Relativistic Reactions -- Four-Force -- Irreducible Decompositions -- The Electromagnetic Field -- Relativistic Angular Momentum -- The Covariant Lorentz Transformation -- Geometric Description of Relativistic Interactions. |
| Record Nr. | UNINA-9910373931203321 |
|
Tsamparlis Michael
|
||
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The special theory of relativity : a mathematical approach / / Farook Rahaman
| The special theory of relativity : a mathematical approach / / Farook Rahaman |
| Autore | Rahaman Farook |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (339 pages) |
| Disciplina | 530.11 |
| Collana | Unitext |
| Soggetto topico |
Mathematical physics
Relativitat especial (Física) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9789811904974
9789811904967 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- About the Author -- 1 Pre-relativity and Galilean Transformation -- 1.1 Failure of Newtonian Mechanics -- 1.2 Galilean Transformations -- 1.3 Galilean Transformations in Vector Form -- 1.4 Non-inertial Frames -- 1.5 Galilean Transformation and Laws of Electrodynamics -- 1.6 Attempts to Locate the Absolute Frame -- 2 Michelson-Morley Experiment and Velocity of Light -- 2.1 Attempts to Locate Special Privileged Frame -- 2.2 The Michelson-Morley Experiment (M-M) -- 2.3 Phenomena of Aberration: Bradley's Observation -- 2.4 Fizeau's Experiment -- 2.5 The Relativistic Concept of Space and Time -- 3 Lorentz Transformations -- 3.1 Postulates of Special Theory of Relativity -- 3.2 Lorentz Transformations -- 3.2.1 Lorentz Transformation Between Two Inertial Frames of Reference (Non-axiomatic Approach) -- 3.2.2 Axiomatic Derivation of Lorentz Transformation -- 3.2.3 Lorentz Transformation Based on the Postulates of Special Theory of Relativity -- 3.3 The General Lorentz Transformations -- 3.4 Thomas Precession -- 4 Mathematical Properties of Lorentz Transformations -- 4.1 Length Contraction (Lorentz-Fitzgerald Contraction) -- 4.2 Time Dilation -- 4.3 Relativity of Simultaneity -- 4.4 Twin Paradox in Special Theory of Relativity -- 4.5 Car-Garage Paradox in Special Theory of Relativity -- 4.6 Real Example of Time Dilation -- 4.7 Terrell Effects -- 5 More Mathematical Properties of Lorentz Transformations -- 5.1 Interval -- 5.2 The Interval Between Two Events Is Invariant Under Lorentz Transformation -- 6 Geometric Interpretation of Space-Time -- 6.1 Space-Time Diagrams -- 6.2 Some Possible and Impossible World Lines -- 6.3 Importance of Light Cone -- 6.4 Relationship Between Space-Time Diagrams in S and S1 Frames.
6.5 Geometrical Representation of Simultaneity, Space Contraction and Time Dilation -- 6.5.1 Simultaneity -- 6.5.2 Space Contraction -- 6.5.3 Time Dilation -- 7 Relativistic Velocity and Acceleration -- 7.1 Relativistic Velocity Addition -- 7.2 Relativistic Velocity Transformations -- 7.3 Relativistic Acceleration Transformations -- 7.4 Uniform Acceleration -- 7.5 Relativistic Transformations of the Direction Cosines -- 7.6 Application of Relativistic Velocity and Velocity Addition Law -- 7.6.1 The Fizeau Effect: The Fresnel's Coefficient of Drag -- 7.6.2 Aberration of Light -- 7.6.3 Relativistic Doppler Effect -- 8 Four-Dimensional World -- 8.1 Four-Dimensional Space-Time -- 8.2 Proper Time -- 8.3 World Velocity or Four Velocities -- 8.4 Lorentz Transformation of Space and Time in Four-Vector Form -- 9 Mass in Relativity -- 9.1 Relativistic Mass -- 9.1.1 First Method Based on Hypothetical Experiment of Tolman and Lews -- 9.1.2 Second Method Based on a Thought Experiment -- 9.1.3 Third Method -- 9.2 Experimental Verification of Relativistic Mass -- 9.3 Lorentz Transformation of Relativistic Mass -- 10 Relativistic Dynamics -- 10.1 Four Forces or Minkowski Force -- 10.2 Four Momenta -- 10.3 Relativistic Kinetic Energy -- 10.4 Mass-Energy Relation -- 10.5 Relation Between Momentum and Energy -- 10.6 Evidence in Support of Mass-Energy Relation -- 10.7 Force in Special Theory of Relativity -- 10.8 Covariant Formulation of Newton's Law -- 10.9 Examples of Longitudinal Mass and Transverse Mass -- 10.10 The Lorentz Transformation of Momentum -- 10.11 The Expression p2 - E2c2 Is Invariant Under Lorentz Transformation -- 11 Photon in Relativity -- 11.1 Photon -- 11.2 Compton Effect -- 11.3 The Lorentz Transformation of Momentum of Photon -- 11.4 Minkowski Force for Photon -- 12 Relativistic Lagrangian and Hamiltonian -- 12.1 Relativistic Lagrangian. 12.2 Relativistic Hamiltonian Function -- 12.3 Covariant Lagrangian and Hamiltonian Formulation -- 12.4 Lorentz Transformation of Force -- 12.5 Relativistic Transformation Formula for Density -- 13 Electrodynamics in Relativity -- 13.1 Relativistic Electrodynamics -- 13.2 Equation of Continuity -- 13.3 Maxwell's Equations -- 13.4 Derivation of Equation of Continuity from Maxwell's Equations -- 13.5 Displacement Current -- 13.6 Transformation for Charge Density -- 13.7 Four Current Vector -- 13.8 Equation of Continuity in Covariant Form -- 13.9 Transformation of Four Current Vector -- 13.10 Maxwell's Equations in Covariant Form -- 13.10.1 The d'Alembertian Operator is Invariant Under Lorentz Transformation -- 13.10.2 Lorentz-Gauge Condition in Covariant Form -- 13.10.3 Gauge Transformations -- 13.11 Transformation of Four Potential Vector -- 13.12 The Electromagnetic Field Tensor -- 13.13 Lorentz Transformation of Electromagnetic Fields -- 13.14 Maxwell's Equations Are Invariant Under Lorentz Transformations -- 13.15 Lorentz Force on a Charged Particle -- 13.16 Electromagnetic Field Produced by a Moving Charge -- 13.17 Relativistic Lagrangian and Hamiltonian Functions … -- 14 Electromagnetic Waves -- 14.1 Introduction -- 14.2 Wave Equation for Magnetic Intensity "0245H -- 14.3 Wave Equation for Electric Field Strength "0245E -- 14.4 Electromagnetic Waves in a Non-conducting Dielectric Medium -- 14.5 Poynting's Theorem (Energy Conservation) -- 14.6 Boundary Conditions -- 14.7 Plane Electromagnetic Waves in a Non-conducting Isotropic Medium -- 14.8 Plane Electromagnetic Waves in a Conducting Medium -- 14.9 Skin Depth -- 14.10 Wave Guides -- 14.11 Coulomb Gauge -- 14.12 Hertz Vector -- 14.13 A Brief Introduction of Relativistic Wave Equation -- 15 Relativistic Mechanics of Continua -- 15.1 Relativistic Mechanics of Continuous Medium (Continua). Appendix Appendix A -- Appendix Appendix B -- Appendix References -- -- Index. |
| Record Nr. | UNISA-996472039003316 |
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Rahaman Farook
|
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| Singapore : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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The special theory of relativity : a mathematical approach / / Farook Rahaman
| The special theory of relativity : a mathematical approach / / Farook Rahaman |
| Autore | Rahaman Farook |
| Edizione | [Second edition.] |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (339 pages) |
| Disciplina | 530.11 |
| Collana | Unitext |
| Soggetto topico |
Mathematical physics
Relativitat especial (Física) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9789811904974
9789811904967 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- About the Author -- 1 Pre-relativity and Galilean Transformation -- 1.1 Failure of Newtonian Mechanics -- 1.2 Galilean Transformations -- 1.3 Galilean Transformations in Vector Form -- 1.4 Non-inertial Frames -- 1.5 Galilean Transformation and Laws of Electrodynamics -- 1.6 Attempts to Locate the Absolute Frame -- 2 Michelson-Morley Experiment and Velocity of Light -- 2.1 Attempts to Locate Special Privileged Frame -- 2.2 The Michelson-Morley Experiment (M-M) -- 2.3 Phenomena of Aberration: Bradley's Observation -- 2.4 Fizeau's Experiment -- 2.5 The Relativistic Concept of Space and Time -- 3 Lorentz Transformations -- 3.1 Postulates of Special Theory of Relativity -- 3.2 Lorentz Transformations -- 3.2.1 Lorentz Transformation Between Two Inertial Frames of Reference (Non-axiomatic Approach) -- 3.2.2 Axiomatic Derivation of Lorentz Transformation -- 3.2.3 Lorentz Transformation Based on the Postulates of Special Theory of Relativity -- 3.3 The General Lorentz Transformations -- 3.4 Thomas Precession -- 4 Mathematical Properties of Lorentz Transformations -- 4.1 Length Contraction (Lorentz-Fitzgerald Contraction) -- 4.2 Time Dilation -- 4.3 Relativity of Simultaneity -- 4.4 Twin Paradox in Special Theory of Relativity -- 4.5 Car-Garage Paradox in Special Theory of Relativity -- 4.6 Real Example of Time Dilation -- 4.7 Terrell Effects -- 5 More Mathematical Properties of Lorentz Transformations -- 5.1 Interval -- 5.2 The Interval Between Two Events Is Invariant Under Lorentz Transformation -- 6 Geometric Interpretation of Space-Time -- 6.1 Space-Time Diagrams -- 6.2 Some Possible and Impossible World Lines -- 6.3 Importance of Light Cone -- 6.4 Relationship Between Space-Time Diagrams in S and S1 Frames.
6.5 Geometrical Representation of Simultaneity, Space Contraction and Time Dilation -- 6.5.1 Simultaneity -- 6.5.2 Space Contraction -- 6.5.3 Time Dilation -- 7 Relativistic Velocity and Acceleration -- 7.1 Relativistic Velocity Addition -- 7.2 Relativistic Velocity Transformations -- 7.3 Relativistic Acceleration Transformations -- 7.4 Uniform Acceleration -- 7.5 Relativistic Transformations of the Direction Cosines -- 7.6 Application of Relativistic Velocity and Velocity Addition Law -- 7.6.1 The Fizeau Effect: The Fresnel's Coefficient of Drag -- 7.6.2 Aberration of Light -- 7.6.3 Relativistic Doppler Effect -- 8 Four-Dimensional World -- 8.1 Four-Dimensional Space-Time -- 8.2 Proper Time -- 8.3 World Velocity or Four Velocities -- 8.4 Lorentz Transformation of Space and Time in Four-Vector Form -- 9 Mass in Relativity -- 9.1 Relativistic Mass -- 9.1.1 First Method Based on Hypothetical Experiment of Tolman and Lews -- 9.1.2 Second Method Based on a Thought Experiment -- 9.1.3 Third Method -- 9.2 Experimental Verification of Relativistic Mass -- 9.3 Lorentz Transformation of Relativistic Mass -- 10 Relativistic Dynamics -- 10.1 Four Forces or Minkowski Force -- 10.2 Four Momenta -- 10.3 Relativistic Kinetic Energy -- 10.4 Mass-Energy Relation -- 10.5 Relation Between Momentum and Energy -- 10.6 Evidence in Support of Mass-Energy Relation -- 10.7 Force in Special Theory of Relativity -- 10.8 Covariant Formulation of Newton's Law -- 10.9 Examples of Longitudinal Mass and Transverse Mass -- 10.10 The Lorentz Transformation of Momentum -- 10.11 The Expression p2 - E2c2 Is Invariant Under Lorentz Transformation -- 11 Photon in Relativity -- 11.1 Photon -- 11.2 Compton Effect -- 11.3 The Lorentz Transformation of Momentum of Photon -- 11.4 Minkowski Force for Photon -- 12 Relativistic Lagrangian and Hamiltonian -- 12.1 Relativistic Lagrangian. 12.2 Relativistic Hamiltonian Function -- 12.3 Covariant Lagrangian and Hamiltonian Formulation -- 12.4 Lorentz Transformation of Force -- 12.5 Relativistic Transformation Formula for Density -- 13 Electrodynamics in Relativity -- 13.1 Relativistic Electrodynamics -- 13.2 Equation of Continuity -- 13.3 Maxwell's Equations -- 13.4 Derivation of Equation of Continuity from Maxwell's Equations -- 13.5 Displacement Current -- 13.6 Transformation for Charge Density -- 13.7 Four Current Vector -- 13.8 Equation of Continuity in Covariant Form -- 13.9 Transformation of Four Current Vector -- 13.10 Maxwell's Equations in Covariant Form -- 13.10.1 The d'Alembertian Operator is Invariant Under Lorentz Transformation -- 13.10.2 Lorentz-Gauge Condition in Covariant Form -- 13.10.3 Gauge Transformations -- 13.11 Transformation of Four Potential Vector -- 13.12 The Electromagnetic Field Tensor -- 13.13 Lorentz Transformation of Electromagnetic Fields -- 13.14 Maxwell's Equations Are Invariant Under Lorentz Transformations -- 13.15 Lorentz Force on a Charged Particle -- 13.16 Electromagnetic Field Produced by a Moving Charge -- 13.17 Relativistic Lagrangian and Hamiltonian Functions … -- 14 Electromagnetic Waves -- 14.1 Introduction -- 14.2 Wave Equation for Magnetic Intensity "0245H -- 14.3 Wave Equation for Electric Field Strength "0245E -- 14.4 Electromagnetic Waves in a Non-conducting Dielectric Medium -- 14.5 Poynting's Theorem (Energy Conservation) -- 14.6 Boundary Conditions -- 14.7 Plane Electromagnetic Waves in a Non-conducting Isotropic Medium -- 14.8 Plane Electromagnetic Waves in a Conducting Medium -- 14.9 Skin Depth -- 14.10 Wave Guides -- 14.11 Coulomb Gauge -- 14.12 Hertz Vector -- 14.13 A Brief Introduction of Relativistic Wave Equation -- 15 Relativistic Mechanics of Continua -- 15.1 Relativistic Mechanics of Continuous Medium (Continua). Appendix Appendix A -- Appendix Appendix B -- Appendix References -- -- Index. |
| Record Nr. | UNINA-9910559393503321 |
|
Rahaman Farook
|
||
| Singapore : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
