Lecture Notes on Quantum Mechanics

by Lindenbaum, Samuel D.

• ISBN13: 9789810238391
• ISBN10: 9810238398
• Format: Hardcover
• Copyright: 1999-06-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

"It is a very useful textbook and a quick reference for those who are interested in the standard and basic mathematical techniques in quantum theory, with some interesting and illustrative examples".Mathematical Reviews

Table of Contents

Preface	v
Contents	vii
Failure of the Classical Theories	1	(12)
Electron-Proton System Collapse	1	(3)
Blackbody Radiation	4	(3)
Planck's Resolution	7	(2)
The Photoelectric Effect	9	(1)
Atomic Spectra	9	(4)
Wave Packets	13	(11)
Space Localization	13	(2)
Uncertainty Relations	15	(1)
Illustrations of Uncertainty Relations	16	(5)
Exercise 1	21	(1)
Exercise 2	22	(2)
Wave Functions and Probability	24	(11)
Physical Interpretation of Wave Packets	24	(2)
Probability	26	(2)
Gaussian Packets	28	(4)
Exercise 3	32	(3)
Schrodinger's Equation	35	(5)
Derivation of Schrodinger's Equation	35	(1)
Differential Conservation Laws	36	(2)
Exercise 4	38	(2)
Quantum Mechanical Operators	40	(11)
Expectation Values	40	(2)
Commutators	42	(6)
General Uncertainty Relation	48	(3)
Schrodinger's Equation with Forces	51	(15)
Introduction of Forces	51	(3)
Energy Eigenvalues and Stationary States	54	(1)
Examples with Forces	55	(7)
Orthogonality and Completeness	62	(4)
Continuous Spectrum Eigensolutions	66	(6)
Completeness	66	(3)
Normalization to Energy	69	(1)
Combination of Discrete and Continuous States	70	(2)
The Harmonic Oscillator	72	(11)
Stationary State Solutions	72	(3)
Hermite Polynomials	75	(5)
Exercise 5	80	(3)
Three-Dimensional Problems	83	(10)
Spherically Symmetric Potential	83	(3)
Angular Momentum	86	(3)
Three-Dimensional Harmonic Oscillator	89	(4)
Matrices	93	(10)
Operator Representations of Matrices	93	(2)
Hermitian Matricies	95	(2)
Matrix Manipulation of the Harmonic Oscillator	97	(3)
Exercise 6	100	(3)
Matrices in Different Representations	103	(10)
Unitary Transformations	103	(3)
Simultaneous Diagonalization of Matrices	106	(2)
Simultaneous Diagonalization for Spherical Symmetry	108	(5)
Approximate Methods I	113	(11)
WKB --- Semi-Classical Approximation	113	(3)
WKB Connection Relations	116	(5)
Exercise 7	121	(3)
Applications of WKB Method	124	(9)
Verification of Bohr Quantum Rules	124	(2)
Proof of Correspondence Principle for Periodic Orbits	126	(4)
Potential Barrier Penetration	130	(3)
Alpha Decay	133	(13)
Introduction	133	(2)
Resonance and Non-Resonance Energy Levels	135	(11)
Approximate Methods II	146	(21)
Time Independent Perturbation Theory	146	(1)
First-Order Approximation	147	(3)
Second-Order Approximation	150	(1)
Degeneracy	151	(5)
Example 1: Normal Zeeman Effect	156	(4)
Exercise 8	160	(7)
Continuous Spectrum Perturbation	167	(13)
Born Approximation	167	(5)
Properties of the Green's Function	172	(2)
Asymptotic Behavior	174	(1)
Spherically Symmetric Potential	175	(3)
Rutherford Scattering	178	(2)
Approximate Methods III	180	(13)
Time Dependent Perturbation Theory	180	(1)
Perturbation Method	181	(2)
Adiabatic Theorem	183	(2)
Non-Adiabatic Limit	185	(1)
Atom in an Excited State	186	(2)
Scattering of Photons by Electrons	188	(5)
Spin and Spinors	193	(20)
Introduction	193	(1)
Formal Properties of Rotation	194	(1)
Infinitesimal Rotation	195	(2)
Finite Rotation in 2-Dimensions	197	(1)
Pauli Spin Matrices	198	(2)
Most General Operator for Spin 1/2	200	(2)
Spinors	202	(1)
Most General 2 x 2 Hermitian Operator	203	(2)
Spin Transformation	205	(6)
Unit Spinors	211	(2)
Fine Structure of the Hydrogen Atom	213	(12)
The Perturbing Potential	213	(3)
Good Quantum Numbers	216	(5)
First-Order Perturbed Energy Levels	221	(4)
Anamolous Zeeman Effect	225	(11)
Introduction	225	(1)
Strong-Field Limit	226	(2)
Weak Field Limit	228	(2)
Transition Region	230	(6)
Assemblages of Identical Particles	236	(17)
Methods of Approach	236	(1)
Assemblage of Bosons	236	(4)
Matrix Elements	240	(3)
Second Quantization	243	(4)
Commutation Relations for Field Variables	247	(3)
Exercise 9	250	(2)
Conclusion	252	(1)
The Dirac Equation	253	(15)
Relativistic Equations	253	(1)
The Dirac Equation	254	(4)
Solution for a Free Particle	258	(2)
Hamiltonian Equation of Motion	260	(4)
Free Electrons --- No Spin Effects	264	(2)
Exercise 10	266	(2)
Non-Relativistic Limits of the Dirac Equation	268	(8)
Large and Small Term Separation of the Dirac Spinor	268	(1)
Expansion to Order υ/c	269	(3)
Expansion to Order υ2/c2	272	(4)
Dirac Operator and Wave Function Transformations	276	(16)
Dirac Equation in Manifestly Covarient Form	276	(2)
Transformation Properties of the Dirac Equation	278	(2)
Charge Current and Density	280	(3)
Example: Free Particle Solution	283	(2)
The Reflection Transformation	285	(3)
Time Reversal	288	(1)
Charge Conjugation	289	(1)
Exercise 11	290	(2)
Negative Energy Solutions; Positron Theory	292	(12)
Introduction to Dirac's Theory of Second Quantization	292	(4)
Symmetrical Formalism for Electrons and Positrons	296	(3)
Annihilation and Creation Operators for Positrons	299	(3)
Vacuum Polarization	302	(2)
Relativistic Theory of Coulomb Scattering	304	(10)
Method 1: Single-Particle Dirac Equation	304	(1)
Method 2: Field Theory	305	(6)
Exercise 12	311	(3)
Compton Scattering	314	(26)
Photon-Electron Interaction	314	(1)
Field Theoretic Approach	315	(2)
Application of Time Dependent Perturbation Theory	317	(4)
Negative Energy Intermediate States	321	(5)
Exercise 13	326	(2)
Feynman Diagrams	328	(1)
Compton Scattering Cross Section	329	(11)
Relativistic and Non-Relativistic Limits	340