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Back-of-the-envelope quantum mechanics : with extensions to many-body systems and integrable PDEs / / Maxim Olshanii, University of Massachusetts Boston, USA
| Back-of-the-envelope quantum mechanics : with extensions to many-body systems and integrable PDEs / / Maxim Olshanii, University of Massachusetts Boston, USA |
| Autore | Olshanii M (Maxim) |
| Pubbl/distr/stampa | New Jersey : , : World Scientific, , [2014] |
| Descrizione fisica | 1 online resource (170 p.) |
| Disciplina | 530.12015118 |
| Soggetto topico | Quantum theory |
| Soggetto genere / forma | Electronic books. |
| ISBN | 981-4508-47-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Ground State Energy of a Hybrid Harmonic-Quartic Oscillator: A Case Study; 1.1 Solved problems; 1.1.1 Dimensional analysis and why it fails in this case; 1.1.1.1 Side comment: dimensional analysis and approximations; 1.1.1.2 Side comment: how to recast input equations in a dimensionless form; 1.1.2 Dimensional analysis: the harmonic oscillator alone; 1.1.3 Order-of-magnitude estimate: full solution; 1.1.3.1 Order-of-magnitude estimates vis-a-vis dimensional analysis; 1.1.3.2 Harmonic vs. quartic regimes; 1.1.3.3 The harmonic oscillator alone
1.1.3.4 The quartic oscillator alone1.1.3.5 The boundary between the regimes and the final result; 1.1.4 An afterthought: boundary between regimes from dimensional considerations; 1.1.5 A Gaussian variational solution; 2. Bohr-Sommerfeld Quantization; 2.1 Solved problems; 2.1.1 A semi-classical analysis of the spectrum of a harmonic oscillator: the exact solution, an order-of-magnitude estimate, and dimensional analysis; 2.1.2 WKB treatment of a "straightened" harmonic oscillator; 2.1.3 Ground state energy in power-law potentials; 2.1.4 Spectrum of power-law potentials 2.1.5 The number of bound states of a diatomic molecule2.1.6 Coulomb problem at zero angular momentum; 2.1.7 Quantization of angular momentum from WKB; 2.1.8 From WKB quantization of 4D angular momentum to quantization of the Coulomb problem; 2.2 Problems without provided solutions; 2.2.1 Size of a neutral meson in Schwinger's toy model of quark confinement; 2.2.2 Bohr-Sommerfeld quantization for periodic boundary conditions; 2.2.3 Ground state energy of multi-dimensional powerlaw potentials; 2.2.4 Ground state energy of a logarithmic potential; 2.2.5 Spectrum of a logarithmic potential 2.2.6 1D box as a limit of power-law potentials2.2.7 Spin-1/2 in the field of a wire; 2.2.8 Dimensional analysis of the time-dependent Schro-dinger equation for a hybrid harmonicquartic oscillator; 2.3 Background; 2.3.1 Bohr-Sommerfeld quantization; 2.3.2 Multi-dimensional WKB; 2.4 Problems linked to the "Background"; 2.4.1 Bohr-Sommerfeld quantization for one soft turning point and a hard wall; 2.4.2 Bohr-Sommerfeld quantization for two hard walls; 3. "Halved" Harmonic Oscillator: A Case Study; Introduction; 3.1 Solved Problems; 3.1.1 Dimensional analysis; 3.1.2 Order-of-magnitude estimate 3.1.3 Another order-of-magnitude estimate3.1.4 Straightforward WKB; 3.1.5 Exact solution; 4. Semi-Classical Matrix Elements of Observables and Perturbation Theory; 4.1 Solved problems; 4.1.1 Quantum expectation value of x6 in a harmonic oscillator; 4.1.2 Expectation value of r2 for a circular Coulomb orbit; 4.1.3 WKB approximation for some integrals involving spherical harmonics; 4.1.4 Ground state wave function of a one dimensional box; 4.1.5 Eigenstates of the harmonic oscillator at the origin: how a factor of two can restore a quantum-classical correspondence 4.1.6 Probability density distribution in a "straightened" harmonic oscillator |
| Record Nr. | UNINA-9910453238903321 |
Olshanii M (Maxim)
|
||
| New Jersey : , : World Scientific, , [2014] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Back-of-the-envelope quantum mechanics : with extensions to many-body systems and integrable PDEs / / Maxim Olshanii, University of Massachusetts, Boston, USA
| Back-of-the-envelope quantum mechanics : with extensions to many-body systems and integrable PDEs / / Maxim Olshanii, University of Massachusetts, Boston, USA |
| Autore | Olshanii M (Maxim) |
| Pubbl/distr/stampa | New Jersey : , : World Scientific, , [2014] |
| Descrizione fisica | 1 online resource (xvii, 151 pages) : illustrations |
| Disciplina | 530.12015118 |
| Collana | Gale eBooks |
| Soggetto topico |
Quantum theory
Many-body problem Differential equations, Partial |
| ISBN | 981-4508-47-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Ground State Energy of a Hybrid Harmonic-Quartic Oscillator: A Case Study; 1.1 Solved problems; 1.1.1 Dimensional analysis and why it fails in this case; 1.1.1.1 Side comment: dimensional analysis and approximations; 1.1.1.2 Side comment: how to recast input equations in a dimensionless form; 1.1.2 Dimensional analysis: the harmonic oscillator alone; 1.1.3 Order-of-magnitude estimate: full solution; 1.1.3.1 Order-of-magnitude estimates vis-a-vis dimensional analysis; 1.1.3.2 Harmonic vs. quartic regimes; 1.1.3.3 The harmonic oscillator alone
1.1.3.4 The quartic oscillator alone1.1.3.5 The boundary between the regimes and the final result; 1.1.4 An afterthought: boundary between regimes from dimensional considerations; 1.1.5 A Gaussian variational solution; 2. Bohr-Sommerfeld Quantization; 2.1 Solved problems; 2.1.1 A semi-classical analysis of the spectrum of a harmonic oscillator: the exact solution, an order-of-magnitude estimate, and dimensional analysis; 2.1.2 WKB treatment of a "straightened" harmonic oscillator; 2.1.3 Ground state energy in power-law potentials; 2.1.4 Spectrum of power-law potentials 2.1.5 The number of bound states of a diatomic molecule2.1.6 Coulomb problem at zero angular momentum; 2.1.7 Quantization of angular momentum from WKB; 2.1.8 From WKB quantization of 4D angular momentum to quantization of the Coulomb problem; 2.2 Problems without provided solutions; 2.2.1 Size of a neutral meson in Schwinger's toy model of quark confinement; 2.2.2 Bohr-Sommerfeld quantization for periodic boundary conditions; 2.2.3 Ground state energy of multi-dimensional powerlaw potentials; 2.2.4 Ground state energy of a logarithmic potential; 2.2.5 Spectrum of a logarithmic potential 2.2.6 1D box as a limit of power-law potentials2.2.7 Spin-1/2 in the field of a wire; 2.2.8 Dimensional analysis of the time-dependent Schro-dinger equation for a hybrid harmonicquartic oscillator; 2.3 Background; 2.3.1 Bohr-Sommerfeld quantization; 2.3.2 Multi-dimensional WKB; 2.4 Problems linked to the "Background"; 2.4.1 Bohr-Sommerfeld quantization for one soft turning point and a hard wall; 2.4.2 Bohr-Sommerfeld quantization for two hard walls; 3. "Halved" Harmonic Oscillator: A Case Study; Introduction; 3.1 Solved Problems; 3.1.1 Dimensional analysis; 3.1.2 Order-of-magnitude estimate 3.1.3 Another order-of-magnitude estimate3.1.4 Straightforward WKB; 3.1.5 Exact solution; 4. Semi-Classical Matrix Elements of Observables and Perturbation Theory; 4.1 Solved problems; 4.1.1 Quantum expectation value of x6 in a harmonic oscillator; 4.1.2 Expectation value of r2 for a circular Coulomb orbit; 4.1.3 WKB approximation for some integrals involving spherical harmonics; 4.1.4 Ground state wave function of a one dimensional box; 4.1.5 Eigenstates of the harmonic oscillator at the origin: how a factor of two can restore a quantum-classical correspondence 4.1.6 Probability density distribution in a "straightened" harmonic oscillator |
| Record Nr. | UNINA-9910790867603321 |
|
Olshanii M (Maxim)
|
||
| New Jersey : , : World Scientific, , [2014] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Back-of-the-envelope quantum mechanics : with extensions to many-body systems and integrable PDEs / / Maxim Olshanii, University of Massachusetts, Boston, USA
| Back-of-the-envelope quantum mechanics : with extensions to many-body systems and integrable PDEs / / Maxim Olshanii, University of Massachusetts, Boston, USA |
| Autore | Olshanii M (Maxim) |
| Pubbl/distr/stampa | New Jersey : , : World Scientific, , [2014] |
| Descrizione fisica | 1 online resource (xvii, 151 pages) : illustrations |
| Disciplina | 530.12015118 |
| Collana | Gale eBooks |
| Soggetto topico |
Quantum theory
Many-body problem Differential equations, Partial |
| ISBN | 981-4508-47-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; 1. Ground State Energy of a Hybrid Harmonic-Quartic Oscillator: A Case Study; 1.1 Solved problems; 1.1.1 Dimensional analysis and why it fails in this case; 1.1.1.1 Side comment: dimensional analysis and approximations; 1.1.1.2 Side comment: how to recast input equations in a dimensionless form; 1.1.2 Dimensional analysis: the harmonic oscillator alone; 1.1.3 Order-of-magnitude estimate: full solution; 1.1.3.1 Order-of-magnitude estimates vis-a-vis dimensional analysis; 1.1.3.2 Harmonic vs. quartic regimes; 1.1.3.3 The harmonic oscillator alone
1.1.3.4 The quartic oscillator alone1.1.3.5 The boundary between the regimes and the final result; 1.1.4 An afterthought: boundary between regimes from dimensional considerations; 1.1.5 A Gaussian variational solution; 2. Bohr-Sommerfeld Quantization; 2.1 Solved problems; 2.1.1 A semi-classical analysis of the spectrum of a harmonic oscillator: the exact solution, an order-of-magnitude estimate, and dimensional analysis; 2.1.2 WKB treatment of a "straightened" harmonic oscillator; 2.1.3 Ground state energy in power-law potentials; 2.1.4 Spectrum of power-law potentials 2.1.5 The number of bound states of a diatomic molecule2.1.6 Coulomb problem at zero angular momentum; 2.1.7 Quantization of angular momentum from WKB; 2.1.8 From WKB quantization of 4D angular momentum to quantization of the Coulomb problem; 2.2 Problems without provided solutions; 2.2.1 Size of a neutral meson in Schwinger's toy model of quark confinement; 2.2.2 Bohr-Sommerfeld quantization for periodic boundary conditions; 2.2.3 Ground state energy of multi-dimensional powerlaw potentials; 2.2.4 Ground state energy of a logarithmic potential; 2.2.5 Spectrum of a logarithmic potential 2.2.6 1D box as a limit of power-law potentials2.2.7 Spin-1/2 in the field of a wire; 2.2.8 Dimensional analysis of the time-dependent Schro-dinger equation for a hybrid harmonicquartic oscillator; 2.3 Background; 2.3.1 Bohr-Sommerfeld quantization; 2.3.2 Multi-dimensional WKB; 2.4 Problems linked to the "Background"; 2.4.1 Bohr-Sommerfeld quantization for one soft turning point and a hard wall; 2.4.2 Bohr-Sommerfeld quantization for two hard walls; 3. "Halved" Harmonic Oscillator: A Case Study; Introduction; 3.1 Solved Problems; 3.1.1 Dimensional analysis; 3.1.2 Order-of-magnitude estimate 3.1.3 Another order-of-magnitude estimate3.1.4 Straightforward WKB; 3.1.5 Exact solution; 4. Semi-Classical Matrix Elements of Observables and Perturbation Theory; 4.1 Solved problems; 4.1.1 Quantum expectation value of x6 in a harmonic oscillator; 4.1.2 Expectation value of r2 for a circular Coulomb orbit; 4.1.3 WKB approximation for some integrals involving spherical harmonics; 4.1.4 Ground state wave function of a one dimensional box; 4.1.5 Eigenstates of the harmonic oscillator at the origin: how a factor of two can restore a quantum-classical correspondence 4.1.6 Probability density distribution in a "straightened" harmonic oscillator |
| Record Nr. | UNINA-9910812655203321 |
|
Olshanii M (Maxim)
|
||
| New Jersey : , : World Scientific, , [2014] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||