LEADER 05379nam 2200637 450 001 9910453238903321 005 20200520144314.0 010 $a981-4508-47-0 035 $a(CKB)2550000001160079 035 $a(EBL)1561246 035 $a(OCoLC)860388605 035 $a(SSID)ssj0001153164 035 $a(PQKBManifestationID)11682140 035 $a(PQKBTitleCode)TC0001153164 035 $a(PQKBWorkID)11151048 035 $a(PQKB)10219428 035 $a(MiAaPQ)EBC1561246 035 $a(WSP)00008811 035 $a(PPN)182135624 035 $a(Au-PeEL)EBL1561246 035 $a(CaPaEBR)ebr10800986 035 $a(CaONFJC)MIL543284 035 $a(EXLCZ)992550000001160079 100 $a20131203h20142014 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBack-of-the-envelope quantum mechanics $ewith extensions to many-body systems and integrable PDEs /$fMaxim Olshanii, University of Massachusetts Boston, USA 210 1$aNew Jersey :$cWorld Scientific,$d[2014] 210 4$dİ2014 215 $a1 online resource (170 p.) 300 $aDescription based upon print version of record. 311 $a981-4508-46-2 311 $a1-306-12033-0 320 $aIncludes bibliographical references and indexes. 327 $aPreface; 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 327 $a1.1.3.4 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 327 $a2.1.5 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 327 $a2.2.6 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 327 $a3.1.3 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 327 $a4.1.6 Probability density distribution in a "straightened" harmonic oscillator 330 $aDimensional and order-of-magnitude estimates are practiced by almost everybody but taught almost nowhere. When physics students engage in their first theoretical research project, they soon learn that exactly solvable problems belong only to textbooks, that numerical models are long and resource consuming, and that ""something else"" is needed to quickly gain insight into the system they are going to study. Qualitative methods are this ""something else"", but typically, students have never heard of them before. The aim of this book is to teach the craft of qualitative analysis using a set of p 606 $aQuantum theory 608 $aElectronic books. 615 0$aQuantum theory. 676 $a530.12015118 700 $aOlshanii$b M$g(Maxim)$0953739 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910453238903321 996 $aBack-of-the-envelope quantum mechanics$92156465 997 $aUNINA LEADER 01266nam 2200361 450 001 9910296455703321 005 20230814230410.0 010 $a1-5386-5599-3 035 $a(CKB)4100000007213052 035 $a(WaSeSS)IndRDA00122701 035 $a(EXLCZ)994100000007213052 100 $a20200507d2018 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$a2018 International Conference on Numerical Simulation of Optoelectronic Devices $e5-9 November 2018, Hong Kong, China /$fIEEE Photonics Society 210 1$aPiscataway, New Jersey :$cInstitute of Electrical and Electronics Engineers,$d2018. 215 $a1 online resource (40 pages) 311 $a1-5386-5600-0 606 $aOptoelectronic devices$xSimulation methods$vCongresses 606 $aNanostructures$vCongresses 615 0$aOptoelectronic devices$xSimulation methods 615 0$aNanostructures 676 $a621.380414 712 02$aIEEE Photonics Society, 801 0$bWaSeSS 801 1$bWaSeSS 906 $aPROCEEDING 912 $a9910296455703321 996 $a2018 International Conference on Numerical Simulation of Optoelectronic Devices$92541461 997 $aUNINA