Quantum Mechanics for Pedestrians 2: Applications and Extensions (Undergraduate Lecture Notes in Physics)

Preface to the Second Edition, Volume 2
Preface to the First Edition, Volume 2
Contents
Contents of Volume 1
Introduction
Overview of Volume 2
Part II Applications and Extensions
15 One-Dimensional Piecewise-Constant Potentials
	15.1 General Remarks
	15.2 Potential Steps
		15.2.1 Potential Step, EV0
	15.3 Finite Potential Well
		15.3.1 Potential Well, E<0
		15.3.2 Potential Well, E>0
	15.4 Potential Barrier, Tunnel Effect
	15.5 From the Finite to the Infinite Potential Well
	15.6 Wave Packets
	15.7 Exercises
16 Angular Momentum
	16.1 Orbital Angular Momentum Operator
	16.2 Generalized Angular Momentum, Spectrum
	16.3 Matrix Representation of Angular Momentum Operators
	16.4 Orbital Angular Momentum: Spatial Representation  of the Eigenfunctions
	16.5 Addition of Angular Momenta
	16.6 Exercises
17 The Hydrogen Atom
	17.1 Central Potential
	17.2 The Hydrogen Atom
	17.3 Complete System of Commuting Observables
	17.4 On Modelling
	17.5 Exercises
18 The Harmonic Oscillator
	18.1 Algebraic Approach
		18.1.1 Creation and Annihilation Operators
		18.1.2 Properties of the Occupation-Number Operator
		18.1.3 Derivation of the Spectrum
		18.1.4 Spectrum of the Harmonic Oscillator
	18.2 Analytic Approach (Position Representation)
	18.3 Exercises
19 Perturbation Theory
	19.1 Stationary Perturbation Theory, Nondegenerate
		19.1.1 Calculation of the First-Order Energy Correction
		19.1.2 Calculation of the First-Order State Correction
	19.2 Stationary Perturbation Theory, Degenerate
	19.3 Hydrogen: Fine Structure
		19.3.1 Relativistic Corrections to the Hamiltonian
		19.3.2 Results of Perturbation Theory
		19.3.3 Comparison with the Results of the Dirac Equation
	19.4 Hydrogen: Lamb Shift and Hyperfine Structure
	19.5 Exercises
20 Entanglement, EPR, Bell
	20.1 Product Space
	20.2 Entangled States
		20.2.1 Definition
		20.2.2 Single Measurements on Entangled States
		20.2.3 Schrödinger's Cat
		20.2.4 A Misunderstanding
	20.3 The EPR Paradox
	20.4 Bell's Inequality
		20.4.1 Derivation of Bell's Inequality
		20.4.2 EPR Photon Pairs
		20.4.3 EPR and Bell
	20.5 Conclusions
	20.6 Exercises
21 Symmetries and Conservation Laws
	21.1 Continuous Symmetry Transformations
		21.1.1 General: Symmetries and Conservation Laws
		21.1.2 Time Translation
		21.1.3 Spatial Translation
		21.1.4 Spatial Rotation
		21.1.5 Special Galilean Transformation
	21.2 Discrete Symmetry Transformations
		21.2.1 Parity
		21.2.2 Time Reversal
	21.3 Exercises
22 The Density Operator
	22.1 Pure States
	22.2 Mixed States
	22.3 Reduced Density Operator
		22.3.1 Example
		22.3.2 Comparison
		22.3.3 General Formulation
	22.4 Exercises
23 Identical Particles
	23.1 Distinguishable Particles
	23.2 Identical Particles
		23.2.1 A Simple Example
		23.2.2 The General Case
	23.3 The Pauli Exclusion Principle
	23.4 The Helium Atom
		23.4.1 Spectrum Without V1,2
		23.4.2 Spectrum with V1,2 (Perturbation Theory)
	23.5 The Ritz Method
	23.6 How Far does the Pauli Principle Reach?
		23.6.1 Distinguishable Quantum Objects
		23.6.2 Identical Quantum Objects
	23.7 Exercises
24 Decoherence
	24.1 A Simple Example
	24.2 Decoherence
		24.2.1 The Effect of the Environment I
		24.2.2 Simplified Description
		24.2.3 The Effect of the Environment II
		24.2.4 Interim Review
		24.2.5 Formal Treatment
	24.3 Time Scales, Universality
	24.4 Decoherence-Free Subspaces, Basis
	24.5 Historical Side Note
	24.6 Conclusions
	24.7 Exercises
25 Scattering
	25.1 Basic Idea; Scattering Cross Section
		25.1.1 Classical Mechanics
		25.1.2 Quantum Mechanics
	25.2 The Partial-Wave Method
	25.3 Integral Equations, Born Approximation
	25.4 Exercises
26 Quantum Information
	26.1 No-Cloning Theorem (Quantum Copier)
	26.2 Quantum Cryptography
	26.3 Quantum Teleportation
	26.4 The Quantum Computer
		26.4.1 Qubits, Registers (Basic Concepts)
		26.4.2 Quantum Gates and Quantum Computers
		26.4.3 The Basic Idea of the Quantum Computer
		26.4.4 The Deutsch Algorithm
		26.4.5 Grover's Search Algorithm
		26.4.6 Shor's Algorithm
		26.4.7 On The Construction of Real Quantum Computers
	26.5 Exercises
27 Is Quantum Mechanics Complete?
	27.1 The Kochen–Specker Theorem
		27.1.1 Value Function
		27.1.2 From the Value Function to Coloring
		27.1.3 Coloring
		27.1.4 Interim Review: The Kochen–Specker Theorem
	27.2 GHZ States
	27.3 Discussion and Outlook
	27.4 Exercises
28 Interpretations of Quantum Mechanics
	28.1 Preliminary Remarks
		28.1.1 Problematic Issues
		28.1.2 Difficulties in the Representation of Interpretations
	28.2 Some Interpretations in Short Form
		28.2.1 Copenhagen Interpretation(s)
		28.2.2 Ensemble Interpretation
		28.2.3 Bohm's Interpretation
		28.2.4 Many-Worlds Interpretation
		28.2.5 Consistent-Histories Interpretation
		28.2.6 Collapse Theories
		28.2.7 Other Interpretations
	28.3 Conclusion
A Abbreviations and Notations
B Special Functions
	B.1 Spherical Harmonics
	B.2 Spherical Bessel Functions
	B.3 Eigenfunctions of the Hydrogen Atom
	B.4 Hermite Polynomials
	B.5 Waves
C Tensor Product
	C.1 Direct Product
	C.2 Direct Sum of Vector Spaces
	C.3 Properties of the Tensor Product
	C.4 Examples
		C.4.1 General Examples
		C.4.2 Example with Reference to Chap.[Entang]20
D Wave Packets
	D.1 General Remarks
		D.1.1 One-Dimensional Wave Packet
		D.1.2 Example: Bell Curve
		D.1.3 Many-Dimensional Wave Packet
	D.2 Potential Step and Wave Packet
	D.3 Exercises
E Laboratory System, Center-of-Mass System
	E.1 The Equivalent One-Body Problem
	E.2 Transformation Laboratory System  Center-of-Mass System
		E.2.1 First Transformation, Then Transition to Quantum Mechanics
		E.2.2 First Transition to Quantum Mechanics,  Then Transformation
F Analytic Treatment of the Hydrogen Atom
	F.1 Nonrelativistic Case: Schrödinger equation
	F.2 Relativistic Case: Dirac equation
		F.2.1 From 4-Spinor to 2-Spinors
		F.2.2 Angular Part of the 2-Spinors
		F.2.3 From 2-Spinors to 4-Spinor
		F.2.4 Coupled Radial Equations, Solution
	F.3 Exercises and Solutions
G The Lenz Vector
	G.1 In Classical Mechanics
	G.2 In Quantum Mechanics
	G.3 General Theorems on Vector Operators
		G.3.1 General Commutator Relations
		G.3.2 Vector Operators
	G.4 Exercises
H Perturbative Calculation of the Hydrogen Atom
	H.1 Calculation of the Matrix Elements
		H.1.1 Matrix Elements of Wmp
		H.1.2 Matrix Elements of Wls
		H.1.3 Matrix Elements of WD
	H.2 Fine Structure Corrections
I The Production of Entangled Photons
	I.1 Atomic Sources
	I.2 Parametric Fluorescence
	I.3 Semiconductor Sources
	I.4 Concluding Remarks
J The Hardy Experiment
	J.1 The Experiment
	J.2 Calculation of the Probabilities
K Set-Theoretical Derivation  of the Bell Inequality
L The Special Galilei Transformation
	L.1 Special Galilei Transformation
		L.1.1 Abstract Notation
		L.1.2 Position Representation
		L.1.3 Several Quantum Objects
	L.2 The Special Galilei Transformation and Kinetic Energy
		L.2.1 One-Dimensional Case
		L.2.2 Three-Dimensional Case
	L.3 Exercises
M Kramers' Theorem
N Coulomb Energy and Exchange Energy  in the Helium Atom
O The Scattering of Identical Particles
P The Hadamard Transformation
	P.1 The MZI and the Hadamard Transformation
	P.2 The Beam Splitter and the Hadamard Transformation
	P.3 The Hadamard Transformation and Quantum Information
Q From the Interferometer to the Computer
R The Grover Algorithm, Algebraically
S Shor Algorithm
	S.1 Classical Part
	S.2 Quantum-Mechanical Part
	S.3 Supplement on Modular Arithmetic
	S.4 Exercises
T The Gleason Theorem
U What is Real? Some Quotations
V Remarks on Some Interpretations of Quantum Mechanics
	V.1 Bohmian Interpretation
		V.1.1 Sketch of the Formalism
		V.1.2 Example: Free Motion
		V.1.3 Conclusions
	V.2 The Many-Worlds Interpretation
	V.3 Consistent Histories
		V.3.1 Definitions
		V.3.2 A Simple Example
		V.3.3 Conclusions
	V.4 Ghirardi-Rimini-Weber
W Elements of Quantum Field Theory
	W.1 Foreword
	W.2 Quantizing a Field - A Toy Example
		W.2.1 The Classical Case
		W.2.2 Quantization
		W.2.3 Creation and Annihilation Operators, Hamiltonian
		W.2.4 Generalization
		W.2.5 Exercises and Solutions
	W.3 Quantization of Free Fields, Introduction
	W.4 Quantization of Free Fields, Klein–Gordon
		W.4.1 Lagrangian, Conjugated Momentum, Poisson Brackets, Hamiltonian
		W.4.2 Canonical Quantization
		W.4.3 Exercises and Solutions
	W.5 Quantization of Free Fields, Dirac
		W.5.1 No Classical Spinor Field
		W.5.2 Lagrangian, Conjugated Momentum, Hamiltonian
		W.5.3 The Free Solutions
		W.5.4 Energy
		W.5.5 Interpretation of br( p)  and  dr( p) , Commutation Relations, Pauli Principle, Number Operator
		W.5.6 Again Infinities
		W.5.7 Anticommutators for Field Operators
		W.5.8 Conclusion
		W.5.9 Exercises and Solutions
	W.6 Quantization of Free Fields, Photons
		W.6.1 Determination of mathcalH
		W.6.2 Determination of H
		W.6.3 Exercises and Solutions
	W.7 Operator Ordering
		W.7.1 Normal Order
		W.7.2 Time Order
		W.7.3 Time Ordering and Normal Ordering
		W.7.4 Exercises and Solutions
	W.8 Interacting Fields, Quantum Electrodynamics
		W.8.1 Lagrangian
		W.8.2 Conjugated Momentum, Hamiltonian
		W.8.3 Interaction Picture, Time Evolution Operator
		W.8.4 S-Operator
		W.8.5 Approximating S
	W.9 S-Matrix, First Order
		W.9.1 Preliminary Note: Virtual Particles
		W.9.2 Field Operators
		W.9.3 Eight Elementary Processes of mathcalHI
		W.9.4 Two Worked Out Examples
		W.9.5 External Fields
		W.9.6 Feynman Diagrams
		W.9.7 First Feynman Rules
		W.9.8 Exercises and Solutions
	W.10 Contraction, Propagator, Wick's Theorem
		W.10.1 Contraction
		W.10.2 Propagators
		W.10.3 Wick's Theorem
		W.10.4 Exercises and Solutions
	W.11 S-Matrix, 2. Order, General
		W.11.1 Applying Wick's Theorem
		W.11.2 Physical Interpretation
	W.12 S-Matrix, 2. Order, 4 Lepton Scattering
		W.12.1 Bhabha Scattering, e+e-rightarrowe+e-
		W.12.2 Møller Scattering, e-e-rightarrowe-e-
		W.12.3 Scattering Cross Section and Feynman Amplitude
		W.12.4 Exercises and Solutions
	W.13 High Precision and Infinities
		W.13.1 Feynman Rules, Diagrams, Amplitudes for QED
		W.13.2 Extraordinary Precision
		W.13.3 Problematic Loops, Infinities, Renormalization
		W.13.4 Conclusion
X Exercises and Solutions
	X.1 Exercises, Chap.15
	X.2 Exercises, Chap.16
	X.3 Exercises, Chap.17
	X.4 Exercises, Chap.18
	X.5 Exercises, Chap.19
	X.6 Exercises, Chap.20
	X.7 Exercises, Chap.[chap21]21
	X.8 Exercises, Chap.22
	X.9 Exercises, Chap.23
	X.10 Exercises, Chap.24
	X.11 Exercises, Chap.25
	X.12 Exercises, Chap.26
	X.13 Exercises, Chap.27
Further Reading
Index of Volume 1
Lake Index
Index of Volume 2
Index