1Introduction to Quantum Theory
164Example 5: Spin Commutator : Example 6: Position/Momentum Uncertainty
21.1 History and Motivation for Quantum Mechanics
165Conclusion
3Early Motivations
166Quantum Dynamics in Three Dimensions
4Other Puzzles Emerge: Quantum Theory Takes Shape
1677.1 Adiabatic Approximations
51.2 Failings of Classical Physics
168Adiabatic Theorem
6Blackbody Radiation
169Example 1: Energy Splitting : Example 2: Spin Precession
7Photoelectric Effect
1707.2 Scattering States
8Compton Scattering: Atomic Spectra
171Scattering Amplitude
91.3 Blackbody Radiation
172Cross Section
10Blackbody Radiation Spectrum
173Scattering Regimes
11Ultraviolet Catastrophe
174Example 3: Scattering by Sphere: Example 4: Rutherford Scattering
12Planck’s Solution
1757.3 Partial Wave Analysis
13Einstein and the Photoelectric Effect
1767.4 Symmetries
14Photoelectric Effect Experiments
177Parity Transformation:
15Einstein’s Explanation Using Photons
178Time-Reversal Symmetry:
16Successes of Photon Model
179Continuous Symmetries and Conservation Laws:: Problems:
171.4 Photoelectric Effect
180Conclusion
18Photoelectric Effect Experiments
181Spin Systems
19Einstein’s Photon Explanation : Successes of the Photon Model
1828.1 Stern-Gerlach Experiment
201.5 Photoelectric Effect
183Experimental Setup:
211.6 Compton Scattering
184Classical Prediction:
22Compton Scattering Experiments
185Observed Result:
23Derivation from Photon Momentum: Implications for Quantum Theory
186Analysis:
241.7 Particle Wave Duality
187Conclusions:
25Evidence for Wave Behavior
188Significance:
26Evidence for Particle Behavior
1898.2 Spin Operators
27The Double Slit Experiment
190Spin-1/2 Operators:
28Failures of Classical Explanations
191Eigenvalues:
29Development of Quantum Theory
192Expectation Values:
30Conclusion
193Uncertainty Principle:
31Mathematical Foundations
194Measuring Spin Components:
322.1 Complex Numbers: Key properties:
195Spin Dynamics:: Problems:
332.2 Linear Algebra
1968.3 Addition of Angular Momentum
34● Vectors and Vector Spaces
1978.4 Identical Particles
35● Matrices
198Bosons:
36● Eigenvalues and Eigenvectors
199Fermions: : Spin Statistics Theorem:
37● Linear Operators and Observables
2008.5 Spin-Orbit Coupling
38Vectors and Vector Spaces
201Relativistic Origin:
39Matrices
202Effects:
40Eigenvalues and Eigenvectors
203Hamiltonian:: Problems:
41Linear Operators and Observables
204Conclusion
422.3 Hilbert Spaces
205Approximation Methods
43Definition:
2069.1 Variational Method
44Operators and Observables:
207Procedure:
45Example 1: Spin Operators : Example 2: Harmonic Oscillator
208Properties:
462.4 Operators: Properties of Quantum Operators:
209Harmonic Oscillator:: Helium Atom:
472.5 Eigenvalue Equations
2109.2 Perturbation Theory
48Example 1: Spin Matrix Eigenvalues
211Consider a Hamiltonian:
49Example 2: Particle in 3D Box
212Eigenvalues:
50Example 3: Quantum Harmonic Oscillator
213Wavefunctions:
51Properties of Eigenvalues and Eigenvectors
214Degenerate Perturbation Theory:: Problems:
52Degenerate Eigenvalues
2159.3 WKB Approximation
53Time Evolution as Eigenvalue Equation
2169.4 Time-Dependent Perturbation Theory
54Conclusion
2179.5 Variational Coupled Cluster : Problems:
55Schrödinger Equation
218Conclusion
563.1 Derivation from Wave Mechanics
219Atomic Structure
573.2 Probabilistic Interpretation
22010.1 Central Force Problems
58Problem 1: Free Particle Wavefunction
221Central Potential:
59Problem 2: Particle in Infinite Well
222Radial Wavefunctions:
60Problem 3: Quantum Harmonic Oscillator
223Angular Wavefunctions:
61Problem 4: Free Particle Spreading
224Quantization:
62Problem 5: Barrier Tunneling Probability
225Spin-Orbit Coupling:
63Problem 6: Linear Harmonic Oscillator
22610.2 Self Consistent Field Method
64Problem 7: Electron in Magnetic Field
227Mean Field Approximation:
65Problem 8: Time-Dependent Perturbations
228Hartree-Fock Equations:
66Problem 9: Step Potential Scattering
229Iterative Procedure:
67Problem 10: Particle in Spherical Potential
230Post-Hartree-Fock Methods:: Problems:
683.3 Eigenfunctions and Eigenvalues
23110.3 Term Symbols
69Example 1: Particle in a Box: Example 2: Harmonic Oscillator
232Notation:
703.4 Mathematical Properties
233Degeneracies:: Fine Structure:
71Normalization
23410.4 Zeeman Effect
72Hermitian Operators
235Hamiltonian:
73Linear Superposition
236Normal Zeeman Effect:
74Completeness
237Anomalous Zeeman Effect: : Paschen-Back Effect:
75Example 3: Normalization
23810.5 Hyperfine Structure
76Example 4: Testing Hermitian
239Hamiltonian: : Problems:
77Example 5: Application of Completeness
240Conclusion
783.5 Time Dependence
241Molecular Structure
79Superposition of States
24211.1 Born-Oppenheimer Approximation
80Probability Densities
24311.2 Hydrogen Molecular Ion
81Example 6: Time Evolution of a Wave Packet: Example 7: Calculating Transition Probabilities
24411.3 Valence Bond Theory
82Conclusion
245Orbital Hybridization
83Quantum Dynamics
246Resonance
844.1 Free Particle Solutions
247Limitations : Mathematics Problems
85Time-Independent Free Particle
24811.4 Molecular Orbital Theory
86Wave Packet Solutions
249Linear Combinations of Atomic Orbitals (LCAO)
87Example 1: Calculating Kinetic Energy: Example 2: Wave Packet Width
250Molecular Orbital Diagrams
884.2 Particle in a Box
251Advantages over Valence Bond Theory: Mathematics Problems
89Time-Independent Solutions
252Conclusion
90Time Dependence
253Electronic Properties of Solids
91Transitions Between States
25412.1 Band Structure
92Example 3: Calculating Transition Rate: Example 4: Wave Packet Dispersion
255Atomic vs Band Structure
934.3 Quantum Tunneling
256Nearly Free Electron Model
94The Curved Potential Barrier
257Brillouin Zones
95Time Dependent Tunneling
258Band Structure of Si and GaAs
96Example 5: Calculate Transmission Probability: Example 6: Compare Classical vs Quantum
259Silicon
974.4 Time-Energy Uncertainty Principle: Example 7: Uncertainty Principle Application
260Gallium Arsenide
984.5 Harmonic Oscillator
261Math Problems
99Time-Independent Solutions
26212.2 Bloch’s Theorem
100Coherent States
263Bloch Wavefunctions
101Time Dependence
264Energy Bands
102Example 1: Energy Spacing: Example 2: Wavepacket Motion
265Band Structure Calculations
1034.6 Tunneling
266Density of States
104Tunneling Probability
267Math Problems
105Time Dependence
26812.3 Tight Binding Model
106Example 3: Calculate Barrier Transmission : Example 4: Wavefunction Evolution
269LCAO Method
1074.7 Numerical Approximation Methods
270Band Structure from Atomic Orbitals: Mathematics Problems
108● Finite Difference Methods
27112.4 Nearly Free Electron Model
109● Split Operator Method
272Classical Free Electron Gas
110Example 5: Finite Difference Grid: Example 6: Quantum Algorithm
273Nearly Free Electron Approximation
111Conclusion
274Limitations: Mathematics Problems
112Three Dimensional Systems
27512.5 Bandgap Materials
1135.1 Schrödinger Equation in Three Dimensions
276Tunable Band Gaps
114Time-Independent SE
277Band Alignment
115Multiple Particles
278Carrier Generation : Mathematics Problems
116Symmetry & Degeneracy: Example 1: Particle in Spherical Potential
279Structural Properties of Solids
1175.2 Quantum Tunneling
28013.1 Crystal Structure
118Rectangular Barrier Tunneling
28113.2 X-ray Diffraction
119Curved Barrier Solutions
28213.3 Lattice Vibrations
120Numerical Methods
28313.4 Phonons
121Example 3: Calculating Barrier Transmission: Example 4: Modeling Wave Function Dynamics
284Conclusion
1225.3 Degeneracy
285Nuclear Physics
123Degeneracy and Symmetry
28614.1 Constituents and Properties: Nuclear properties:
124Perturbation theory
28714.2 Nuclear Force and Models: Example nuclear physics problems:
125Degenerate Systems
28814.3 Radioactive Decay
126Example 5: Quantize Monoatomic Ideal Gas: Example 6: Photon Polarizations
28914.4 Nuclear Reactions : Examples of nuclear reaction problems:
1275.4 Hydrogen Atom Solutions
290Conclusion
128Quantum Numbers
291Particle Physics
129Degeneracy
29215.1 Standard Model Fundamentals
130Stark Effect
293Fundamental Particles
131Example 1: Probability Density: Example 2: Stark Shift
294Fundamental Forces
1325.5 Angular Momentum
295Symmetries and Conservation Laws: Problems
133Orbital Angular Momentum
29615.2 Quarks
134Spin Angular Momentum
297Quark Color Charges & Gluons
135Adding Angular Momentum
298Quark Confinement
136Example 3: Spin 1/2 Measurement: Example 4: Spin Coupling
299Quark Matter Phases: Problems
1375.5 Spin
30015.3 Gauge Symmetries
138Spin Operators
30115.4 Grand Unification Theories: Problems
139Spin Magnitude
302Conclusion
140Stern-Gerlach Experiment
303Frontiers of Quantum Mechanics
141Example 5: Spin 1/2 Measurement: Example 6: Maximum Spin Projection
30416.1 Quantum Information Science
142Conclusion
305Qubits:
143Mathematical Tools of Quantum Mechanics
306Quantum registers and gates:
1446.1 Dirac Notation: Kets and Bras
307Quantum measurement:
1456.2 State Vectors and Bra-Ket Notation
308Quantum entanglement:
146● Ket Notation
309Quantum algorithms: : Quantum error correction (QEC):
147● Bra Vectors
310Quantum Information Science Experiments and Applications
148● Expansion Postulate
311Superconducting Qubits:
149Example 1: State Representation: Example 2: Expectation Value
312Trapped Ions: : Photonics:
1506.3 Operators
313Quantum Error Correction Codes and Fault Tolerance : Problems
151Observable Operators
31416.2 Quantum Computing
152Hermitian Operators
315Physical Implementation Platforms
153Matrix Representations
316Superconducting Qubits:-
154Example 1: Eigenvalue Equation: Example 2: Spin Operator Sz
317Trapped Ions:-
1556.4 Expectation Values
318Photonics:-
156Expectation Value Definition
319Quantum Software Stack and Applications: Problems
157Interpretation
32016.3 Quantum Cryptography: Problems
158Uncertainty Relation
32116.4 Entanglement : Problems
159Example 3: Energy Expectation Value : Example 4: Position Uncertainty
32216.5 Bell’s Inequality : Problems
1606.5 Commutators
323Conclusion
161Definition
324Glossary
162Non-Commuting Operators
325Index
163Heisenberg Uncertainty Principle
