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Summary Pages

• First Day Lecture PDF, PPT

• Changing Bases - Ch 2 Material

• Summary of State Vectors, PDF - for Ch 1-2

• Angular Momentum Summary, PDF - for Ch 3-5

• Spin Eigenstates Review (Printable, Handout)

• One-dimensional Schrödinger  Equation - for Ch 6

• Finite Square Well - summary - updated 10/13/21

• Perturbative and WKB Expansions - Supplement for Ch 6

• L-Squared - Ch 9, Also, Levi-Civita Symbol

• 3D Schrödinger - for Ch 9-10

• Perturbation Theory - Summary and Presentation

• Blackboards - Fall 2024 and 2022

• Dirac Equation - with clips of Dirac (29:05)
• Dirac Lectures (59:58)
• Interview with Dirac (20:33)

Sample Exams

• Review I, Sample Exam I

• Review II, Sample Exam II

• Review for Final, Sample Final Exam

Stern-Gerlach Experiment

• First Day Lecture PDF, PPT

• Old Quantum Theory - Wkipedia

Stern-Gerlach Experiment - Hyperphysics

• Particle Spin and the Stern-Gerlach Experiment

• Simulink - SG on Last pages

• Quantum States and the Bloch sphere

•  "Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics"

• A century ago the Stern-Gerlach experiment ruled unequivocally in favor of Quantum Mechanics
• Feynman's modified SG device

Gaussian Units

• Gaussian Units Handout

• Unit Converter

• Conversion Table

• Longer discussion

• A Note on Units

EPR and Quantum Computing (See QC Links)

• EPR Paper: Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?

• Bohr's Response

• Bell, Bohm, and qubit: EPR remixed (202) AJP Paper

• Tensor Product

• Qubits, Quantum Mechanics, and Computers - Lecture Notes

• Entanglement — QComputing, EPR, and Bell - Allan Adams MIT Lecture (1:22:44)

• Bell's Inequality: The weirdest theorem in the world | Nobel Prize 2022 (13:21) - Simple explanation
• Nobel 2022: Alain Aspect, John F. Clauser and Anton Zeilinger "for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science"
• Zellinger acceptance speech (36:22)
• Clauser acceptance speech (40:19)
• Aspect acceptance speech (37:46)
• Anton Zeilinger – Breaking the Wall of Illusion (17:00)

• Here are some links to quantum computers.

  • https://phys.org/news/2021-07-team-quantum-simulator-qubits-largest.html 
    Team develops quantum simulator with 256 qubits, largest of its kind ever created

  • https://www.theverge.com/2021/5/19/22443453/google-quantum-computer-2029-decade-commercial-useful-qubits-quantum-transistor 
    Google wants to build a useful quantum computer by 2029

  • https://research.ibm.com/blog/ibm-quantum-roadmap  1,000-qubit chip, IBM Quantum Condor, targeted for the end of 2023.

  • https://techwireasia.com/2021/07/the-quantum-computing-race-is-heating-up-as-the-chinese-surpass-google/  The quantum computing race is heating up as the Chinese surpass Google – 66-qubit vs 54 qubit (in 2019)

  • IBM https://quantum-computing.ibm.com/login 
    Microsoft, IBM and Google have all created tools — Q#, Qiskit and Cirq

  • How to get started in quantum computing - https://www.nature.com/articles/d41586-021-00533-x

  • Quirk Circuit

  • Introduction to Quantum Computing and Quantum Hardware at Qiskit

  • Quantum Computing IBM

• Alice & Bob A History of The World’s Most Famous Cryptographic Couple

• Marissa Giustina: Significant loophole-free test of Bell’s theorem with entangled photons

• Dancing with Qubits

1D Schrödinger Equation

• Finite Square Well - Hyperphysics

• Tunneling thru Square Potential Barrier - Maple Worksheet

• Delta function potential

• Revisiting the double delta function potential

• Videos

  • Free Particle - Donny Lee

  • Finite Square Well

  • Delta function bound state, scattering

  • Tunneling through barrier

• Alpha Decay

  • Hyperphysics discussion

  • Polonium 212 decay

  • U-235 Decay Chain, U-232 Chain

  • KE of alpha particle

  • Scattering, Tunneling and Alpha Decay

  • Video showing full computation (50:28), Another derivaton (44:10)

  • Gamow's 1928 (Eng) and Fowler and Wilson 1929 - papers on alpha decay

  • The Early History of Quantum Tunneling

  • Gamow’s Theory of Alpha-Decay

  • Gamows alpha decay theory revisited - preprint

• Numerical Solutions

  • Finite-Difference Time-Domain Algorithm at SciPy Cookbook

  • MATLAB code

    • Code from class

      Time-independent SE, TISE.m

      Time-dependent SE, TDSE.m

    • Some other code: quantumscatter.m

  • pySchrodinger - Python animation

    Download animate_schrodinger.py, schrodinger.py

    Run the first. In Spyder, just use F10 to animate

  • Quantum Optics Julia

  Numerov Method

  • Short animation and link to some Python code

  • Solving 1D SE in Python Github

  • Solving 1-D Schrodinger Equation in Python

  • MATLAB codes for teaching quantum physics: Part 1

  • Physlet Quantum Physics - See Animations

    • Wavepackets

    • Infinite Square Well

    • Finite Square Well

    • Scattering

Quantum Harmonic Oscillator

• Quantum Oscillator or Later Version - MIT Opencourseware

• Algebraic Method

• A completely algebraic solution of the simple harmonic oscillator - contains history of solution of QHO

• Hermite Polynomials

• Lecture on Coherent States (22:45)

• Plotting

  • Maple - QHO.mws, qsho.mws 

• Coherent State - Maple coherent.mw, html, MATLAB Livescript CoherentState.mlx

• E. C. G. Sudarshan and his Diagonal Representation in Quantum Optics

• Perturbative and WKB Expansions Anharmonic oscillator

Path Intergals

• Feynman's Thesis and a video
• Feyman and Hibbs Dover Edition
• The Errors of Feynman and Hibbs - D. F. Styer
• Deriving The Feynman Path Integral Part 1 (12:20) and Part 2 (38:27)
• Feynman Path Integrals I (33:07)
• Feynman Path Integrals II (31:10) Computational Physics
• Classical physics derived from quantum mechanics: Feynman Path Integral (52:28)

Spherical Harmonics

• Spherical Harmonics 3D

• Spherical Harmonics Nodes

• Spherical Harmonics Contours

• Visualizing atomic orbitals using Mathematica

Radial Wavefunctions

• Electron Configurations

  • Hydrogren Atom

  • Electron Configuration

• Nuclear Shell model

  • Hyperphysics

  • Nuclear Shell Model and Magic Numbers

  • Ordering of Energy Levels

    • 1965 E. Segre, Nuclei & Particles - 1st Ed p. 250 [2nd ed. p. 286]

    • 1959 R. B. Leighton, Principles of Modern Physics, p. 603, at HaithiTrust

    • Feld, 1953 - Original Table

• Spherical Bessel Functions and zeros

• The Shell Model of the Nucleus - slides

Perturbation Theory

• Class Notes: Perturbation Theory - Summary and Presentation

• Nondegenerate perturbation theory,

• Degenerate perturbation theory  and

• Perturbation theory, problem solving 

• Hydrogen fine structure

• Fine Structure, Hyperfine Structure

• Zeeman Effect

• Stark Effect

• Lamb shift

• The Lamb Shift - Freeman Dyson Story Video (5:44)

• Time Independent Perturbation Theory - MIT

  • General Problem (22:56)

  • Setting Up Equations (16:09)

  • Energy Corrections (6:27)

  • First order correction to the state. Second order correction to energy (13:45)

  • Validity (22:28)

  • Anharmonic Oscillator (20:56)

  • Degenerate Perturbation theory (25:21)

• Perturbation methods for algebraic equations - Strogatz (1:13:48)

• WKB Approximation

  • Perturbative and WKB Expansions  - Herman

  • Derivation

  • An Elementary Introduction to the JWKB Approximation

Miscellaneous

• The Quantum Exchange

• Susskind's 2012 Lectures on QM

• Feynman Lectures Volume III

• Additional Readings

• Spin Operators and Matrices

• Lectures on QM I, QM II  

• Geometric Algebra for Electrical and Electronic Engineers

Other Sources

• Prof. Broholm's Review Lecture

• Johns Hopkins Course

• UNM Courses I, II

Maple Files