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Handouts

• First Day Lecture PDF, PPT

• Changing Bases - Ch 2 Material

• Summary of State Vectors - for Ch 1-2

• Angular Momentum Summary - for Ch 3-5

• Spin Eigenstates Review (Printable, Handout)

• One-dimensional Schrödinger  Equation - for Ch 6

• Time Evolution of a Gaussian - for Ch 6

• Finite Square Well - Summary - for Ch 6

• Perturbative and WKB Expansions - Supplement for Ch 6

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

• 3D Schrödinger - for Ch 9-10

• Perturbation Theory - Summary and Presentation - for Ch 11

• Blackboards - Fall 2024 and 2022

Sample Exams

• Review I, Sample Exam I

• Review II, Sample Exam II

• Review for Final, Sample Final Exam

Early Quantum Mechanics History

• First Day Lecture PDF
• Old Quantum Theory - Wkipedia
• The Hidden Story behind Max Planck's Discovery of QM (21:10)
• Planck, Oct 19, 1900 in German, English
• Planck, Dec 14 1900, English
• Planck's 1901 Paper, AI Generated reading (14:09)
• Wien, 1896 in German
• Rubens, H. & Kurlbaum, F., 1901 - Failure of Wein Radiation Law
• A derivation of Balmer’s formula

Stern-Gerlach Experiment

• Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics
• Stern-Gerlach Experiment - Hyperphysics
• Simulink - See SG models on pages 15-18
• Quantum States and the Bloch sphere
• A century ago the Stern-Gerlach experiment ruled unequivocally in favor of Quantum Mechanics
• Feynman's modified SG device - Feynman Lectures Vol. III, Ch 5

Gaussian Units

• Gaussian Units Handout

• Unit Converter

• Conversion Table

• A Note on Units

EPR and Quantum Computing (See QC Links for more)

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

• Bohr's Response

• The Tensor Product, Demystified

• Bell's Inequality
• Entanglement — QComputing, EPR, and Bell - MIT Lecture (1:22:44)
• Bell's Inequality: The weirdest theorem in the world (13:21) - Simple explanation

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

• Bell nonlocality - Rev. Mod. Phys. Vol. 86, 2014.

• Marissa Giustina: Significant loophole-free test of Bell’s theorem with entangled photons (1:16:36)

• Micius quantum experiments in space - Rev. Mod. Phys. Vol. 94 2022
• 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"
• Aspect acceptance speech (37:46)
• Clauser acceptance speech (40:19)
• Zellinger acceptance speech (36:22)
• Anton Zeilinger – Breaking the Wall of Illusion (17:00)

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

• Birth: 1978
• The Alice and Bob After Dinner Speech
• "The Talk" - A comic on quantum computing

1D Schrödinger Equation

• Phase, Group and Signal Velocity

• 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 (5:52)

  • Finite Square Well (24:31)

  • Delta function bound state (18:50), scattering (24:14)

  • Tunneling through barrier (4:15)

• Alpha Decay

  • Hyperphysics discussion

  • Polonium 212 decay

  • U-235 Decay Chain, U-232 Chain

  • KE of alpha particle Polonium decay

  • Scattering, Tunneling and Alpha Decay

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

  • Gamow's 1928 paper (Eng)
  • Fowler and Wilson 1929 paper

  • The Early History of Quantum Tunneling - Merzbacher, Physics Today, December 2001, page 35.

  • Gamow’s Theory of Alpha-Decay

  • Gamow, Alpha Decay, and the Liquid-Drop Model of the Nucleus

  • 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
    • Python examples Github

  • 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

  • Solving the Time Dependent Schrodinger Equation with Physics-Informed Deep Learning

Quantum Harmonic Oscillator

• Quantum Oscillator (1:20:59) or Shorter Version (16:41) - MIT Opencourseware

• Algebraic Method (39:45)

• 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 Integrals

• Feynman's Thesis and a video (15:11)
• 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)

Visualize 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,
      See diagram at at HaithiTrust

    • Feld, 1953 - Original Table

• Spherical Bessel Functions and zeros

Perturbation Theory

• Class Notes: Perturbation Theory - Summary and Presentation

• 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

Dirac Equation

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

Miscellaneous

• The Quantum Exchange

• Susskind's 2012 Lectures on QM

• Feynman Lectures Volume III

• Additional Readings

• Spin Operators and Matrices

• Geometric Algebra for Electrical and Electronic Engineers

• UNM Courses I, II

Maple Files