Quantum Mechanics Classical Results, Modern Systems, and Visualized Examples

by Robinett, Richard

• ISBN13: 9780198530978
• ISBN10: 0198530978
• Edition: 2nd
• Format: Hardcover
• Copyright: 2006-06-22
• Publisher: Oxford University Press

Summary

The Concise Oxford History of Indian Business is an adapted edition of The Oxford History of Business. The author traces the transformation of the Indian business class from merchants to industrialists and, more recently, service providers. The focus of this volume is on the modern or that phase of Indian business in free India and response of Indian business to the call of globalization.

Author Biography

Richard W. Robinett
Professor of Physics, Penn State University
University Park, PA 16802
USA Undergraduate majors in Mathematics and Physics (Magna cum laude)
from the University of Minnesota 1975
Ph. D. (elementary particle theory, grand unified theories) from
University of Minnesota, 1981
Postdoctoral research positions at University of Wisconsin, Madison
(1981-1983) and University of Massachusetts, Amherst (1803-1986)
Assistant, Associate, and then Full Professor in the Department of
Physics, Penn State University
Assistant/Associate Department Head, Physics Department, Penn State
University, 1999 - present Elected Fellow of the American Physical Society (Forum on Education) 2003
Robinett, Richard W
Penn State University
Citation: For his contributions to undergraduate education in quantum mechanics, especially in visualization, and for demonstrated excellence in the training and advising of undergraduate physics majors.
Nominated by: Forum on Education

Table of Contents

Part I The Quantum Paradigm	1	(412)
A First Look at Quantum Physics	3	(31)
How this Book Approaches Quantum Mechanics	3	(5)
Essential Relativity	8	(2)
Quantum Physics: h as a Fundamental Constant	10	(7)
Semiclassical Model of the Hydrogen Atom	17	(4)
Dimensional Analysis	21	(2)
Questions and Problems	23	(11)
Classical Waves	34	(31)
The Classical Wave Equation	34	(2)
Wave Packets and Periodic Solutions	36	(7)
General Wave Packet Solutions	36	(2)
Fourier Series	38	(5)
Fourier Transforms	43	(3)
Inverting the Fourier transform: the Dirac δ-function	46	(5)
Dispersion and Tunneling	51	(6)
Velocities for Wave Packets	51	(2)
Dispersion	53	(3)
Tunneling	56	(1)
Questions and Problems	57	(8)
The Schrodinger Wave Equation	65	(19)
The Schrodinger Equation	65	(2)
Plane Waves and Wave Packet Solutions	67	(8)
Plane Waves and Wave Packets	67	(3)
The Gaussian Wave Packet	70	(5)
``Bouncing'' Wave Packets	75	(2)
Numerical Calculation of Wave Packets	77	(2)
Questions and Problems	79	(5)
Interpreting the Schrodinger Equation	84	(50)
Introduction to Probability	84	(7)
Discrete Probability Distributions	84	(3)
Continuous Probability Distributions	87	(4)
Probability Interpretation of the Schrodinger Wavefunction	91	(5)
Average Values	96	(6)
Average Values of Position	96	(2)
Average Values of Momentum	98	(2)
Average Values of Other Operators	100	(2)
Real Average Values and Hermitian Operators	102	(2)
The Physical Interpretation of Φ (p)	104	(3)
Energy Eigenstates, Stationary States, and the Hamiltonian Operator	107	(4)
The Schrodinger Equation in Momentum Space	111	(5)
Transforming the Schrodinger Equation Into Momentum Space	111	(3)
Uniformly Accelerating Particle	114	(2)
Commutators	116	(2)
The Wigner Quasi-Probability Distribution	118	(3)
Questions and Problems	121	(13)
The Infinite Well: Physical Aspects	134	(32)
The Infinite Well in Classical Mechanics: Classical Probability Distributions	134	(3)
Stationary States for the Infinite Well	137	(9)
Position-Space Wavefunctions for the Standard Infinite Well	137	(3)
Expectation Values and Momentum-Space Wavefunctions for the Standard Infinite Well	140	(4)
The Symmetric Infinite Well	144	(2)
The Asymmetric Infinite Well	146	(5)
Time-Dependence of General Solutions	151	(6)
Two-State Systems	151	(3)
Wave Packets in the Infinite Well	154	(3)
Wave Packets Versus Stationary States	157	(1)
Questions and Problems	157	(9)
The Infinite Well: Formal Aspects	166	(26)
Dirac Bracket Notation	166	(1)
Eigenvalues of Hermitian Operators	167	(1)
Orthogonality of Energy Eigenfunctions	168	(3)
Expansions in Eigenstates	171	(4)
Expansion Postulate and Time-Dependence	175	(6)
Parity	181	(2)
Simultaneous Eigenfunctions	183	(2)
Questions and Problems	185	(7)
Many Particles in the Infinite Well: The Role of Spin and Indistinguishability	192	(18)
The Exclusion Principle	192	(1)
One-Dimensional Systems	193	(2)
Three-Dimensional Infinite Well	195	(3)
Applications	198	(8)
Conduction Electrons in a Metal	198	(2)
Neutrons and Protons in Atomic Nuclei	200	(1)
White Dwarf and Neutron Stars	200	(6)
Questions and Problems	206	(4)
Other One-Dimensional Potentials	210	(29)
Singular Potentials	210	(11)
Continuity of ψ (x)	210	(2)
Single δ-function Potential	212	(1)
Twin δ-function Potential	213	(3)
Infinite Array of δ-functions: Periodic Potentials and the Dirac Comb	216	(5)
The Finite Well	221	(9)
Formal Solutions	221	(4)
Physical Implications and the Large x Behavior of Wavefunctions	225	(5)
Applications to Three-Dimensional Problems	230	(4)
The Schrodinger Equation in Three Dimensions	230	(1)
Model of the Deuteron	231	(3)
Questions and Problems	234	(5)
The Harmonic Oscillator	239	(21)
The Importance of the Simple Harmonic Oscillator	239	(4)
Solutions for the SHO	243	(6)
Differential Equation Approach	243	(4)
Properties of the Solutions	247	(2)
Experimental Realizations of the SHO	249	(2)
Classical Limits and Probability Distributions	251	(3)
Unstable Equilibrium: Classical and Quantum Distributions	254	(1)
Questions and Problems	255	(5)
Alternative Methods of Solution and Approximation Methods	260	(47)
Numerical Integration	261	(5)
The Variational or Rayleigh-Ritz Method	266	(7)
The WKB method	273	(5)
WKB Wavefunctions	274	(3)
WKB Quantized Energy Levels	277	(1)
Matrix Methods	278	(8)
Perturbation Theory	286	(13)
Nondegenerate States	286	(7)
Degenerate Perturbation Theory	293	(2)
Time-Dependent Perturbation Theory	295	(4)
Questions and Problems	299	(8)
Scattering	307	(26)
Scattering in One-Dimensional Systems	307	(3)
Bound and Unbound States	307	(3)
Plane Wave Solutions	310	(1)
Scattering from a Step Potential	310	(5)
Scattering from the Finite Square Well	315	(6)
Attractive Well	315	(4)
Repulsive Barrier	319	(2)
Applications of Quantum Tunneling	321	(9)
Field Emission	321	(3)
Scanning Tunneling Microscopy	324	(1)
α-Particle Decay of Nuclei	325	(3)
Nuclear Fusion Reactions	328	(2)
Questions and Problems	330	(3)
More Formal Topics	333	(37)
Hermitian Operators	333	(4)
Quantum Mechanics, Linear Algebra, and Vector Spaces	337	(4)
Commutators	341	(2)
Uncertainty Principles	343	(3)
Time-Dependence and Conservation Laws in Quantum Mechanics	346	(6)
Propagators	352	(5)
General Case and Free Particles	352	(1)
Propagator and Wave Packets for the Harmonic Oscillator	353	(4)
Timescales in Bound State Systems: Classical Period and Quantum Revival Times	357	(3)
Questions and Problems	360	(10)
Operator and Factorization Methods for the Schrodinger Equation	370	(14)
Factorization Methods	370	(1)
Factorization of the Harmonic Oscillator	371	(6)
Creation and Annihilation Operators	377	(3)
Questions and Problems	380	(4)
Multiparticle Systems	384	(29)
Generalities	384	(3)
Separable Systems	387	(2)
Two-Body Systems	389	(5)
Classical Systems	390	(1)
Quantum Case	391	(3)
Spin Wavefunctions	394	(2)
Indistinguishable Particles	396	(11)
Questions and Problems	407	(6)
Part II The Quantum World	413	(228)
Two-Dimensional Quantum Mechanics	415	(33)
2D Cartesian Systems	417	(6)
2D Infinite Well	418	(4)
2D Harmonic Oscillator	422	(1)
Central Forces and Angular Momentum	423	(6)
Classical Case	423	(2)
Quantum Angular Momentum in 2D	425	(4)
Quantum Systems with Circular Symmetry	429	(8)
Free Particle	429	(3)
Circular Infinite Well	432	(3)
Isotropic Harmonic Oscillator	435	(2)
Questions and Problems	437	(11)
The Schrodinger Equation in Three Dimensions	448	(53)
Spherical Coordinates and Angular Momentum	449	(5)
Eigenfunctions of Angular Momentum	454	(13)
Methods of Derivation	454	(9)
Visualization and Applications	463	(2)
Classical Limit of Rotational Motion	465	(2)
Diatomic Molecules	467	(8)
Rigid Rotators	467	(2)
Molecular Energy Levels	469	(3)
Selection Rules	472	(3)
Spin and Angular Momentum	475	(7)
Addition of Angular Momentum	482	(9)
Free Particle in Spherical Coordinates	491	(1)
Questions and Problems	492	(9)
The Hydrogen Atom	501	(39)
Hydrogen Atom Wavefunctions and Energies	501	(6)
The Classical Limit of the Quantum Kepler Problem	507	(6)
Other ``Hydrogenic'' Atoms	513	(4)
Rydberg Atoms	513	(2)
Muonic Atoms	515	(2)
Multielectron Atoms	517	(12)
Helium-Like Atoms	519	(5)
Lithium-Like Atoms	524	(3)
The Periodic Table	527	(2)
Questions and Problems	529	(11)
Gravity and Electromagnetism in Quantum Mechanics	540	(56)
Classical Gravity and Quantum Mechanics	540	(3)
Electromagnetic Fields	543	(7)
Classical Electric and Magnetic Fields	543	(5)
E and B Fields in Quantum Mechanics	548	(2)
Constant Electric Fields	550	(2)
Atoms in Electric Fields: The Stark Effect	552	(9)
Classical Case	552	(3)
Quantum Stark Effect	555	(6)
Constant Magnetic Fields	561	(3)
Atoms in Magnetic Fields	564	(12)
The Zeeman Effect External B Fields	564	(5)
Spin-Orbit Splittings: Internal B Fields	569	(5)
Hyperfine Splittings: Magnetic Dipole-Dipole Interactions	574	(2)
Spins in Magnetic Fields	576	(7)
Measuring the Spinor Nature of the Neutron Wavefunction	576	(2)
Spin Resonance	578	(5)
The Aharonov-Bohm Effect	583	(3)
Questions and Problems	586	(10)
Scattering in Three Dimensions	596	(45)
Classical Trajectories and Cross-Sections	597	(6)
Quantum Scattering	603	(9)
Cross-Section and Flux	603	(3)
Wave Equation for Scattering and the Born Approximation	606	(6)
Electromagnetic Scattering	612	(7)
Partial Wave Expansions	619	(5)
Scattering of Particles	624	(11)
Frames of Reference	625	(6)
Identical Particle Effects	631	(4)
Questions and Problems	635	(6)
A. Dimensions and MKS-type Units for Mechanics, Electricity and Magnetism, and Thermal Physics	641	(3)
Problems	642	(2)
B. Physical Constants, Gaussian Integrals, and the Greek Alphabet	644	(5)
Physical Constants	644	(2)
The Greek Alphabet	646	(1)
Gaussian Probability Distribution	646	(2)
Problems	648	(1)
C. Complex Numbers and Functions	649	(4)
Problems	651	(2)
D. Integrals, Summations, and Calculus Results	653	(13)
Integrals	653	(5)
Summations and Series Expansions	658	(3)
Assorted Calculus Results	661	(1)
Real Integrals by Contour Integration	661	(3)
Plotting	664	(1)
Problems	665	(1)
E. Special Functions	666	(8)
Trigonometric and Exponential Functions	666	(1)
Airy Functions	667	(1)
Hermite Polynomials	668	(1)
Cylindrical Bessel Functions	669	(1)
Spherical Bessel Functions	669	(1)
Legendre Polynomials	669	(1)
Generalized Laguerre Polynomials	670	(1)
The Dirac δ-Function	671	(1)
The Euler Gamma Function	672	(1)
Problems	672	(2)
F. Vectors, Matrices, and Group Theory	674	(6)
Vectors and Matrices	674	(5)
Group Theory	679	(1)
Problems	679	(1)
G. Hamiltonian Formulation of Classical Mechanics	680	(7)
Problems	685	(2)
References	687	(8)
Index	695