Course Outline

Phys 231 is an overview of modern physics with a strong emphasis on quantum theory and its applications. Quantum theory was developed in the early twentieth century in response to several observed phenomena which could not be described by classical physics. This theory successfully solved many outstanding problems, particularly those related to physics at the microscopic level, and currently provides the broadest understanding of the physical world at the most fundamental levels. A majority of physics research activity today involves quantum theory in some form. Quantum theory is essential for understanding how elements of modern technology such as lasers, semiconductors, superconductors, nuclear reactors, and magnetic resonance operate. It also gives rise to many apparently bizarre phenomena, which are completely counter-intuitive and inexplicable from your everyday classical perspective. Almost a century after its invention, experts still do not agree on the interpretation of such fundamental features as measurement or preparation of a quantum system.

The course will cover the following topics subject to minor modifications.

  1. Historical quantum physics phenomena.
  2. Particle diffraction and matter waves.
  3. One dimensional Schrodinger equation and applications such as confined particles.
  4. Three dimensional Schrodinger equation, angular momentum and the hydrogen atom.
  5. Identical particles.
  6. Spin-1/2 particles.
  7. Selected applications of quantum physics.

Homework Assignments

Due: January 28, 2026 Homework 1
Due: February 2, 2026 Homework 2
Due: February 9, 2026 Homework 3
Due: February 16, 2026 Homework 4
Due: February 25, 2026 Homework 5
Due: March 2, 2026 Homework 6
Due: March 9, 2026 Homework 7
Due: March 25, 2026 Homework 8
Due: April 6, 2026 Homework 9
Due: April 13, 2026 Homework 10
Due: April 20, 2026 Homework 11
Due: April 29, 2026 Homework 12
Due: May 8, 2026 Homework 13

Exams

There will be three exams during class on the following dates: Friday, February 20, 2026, Monday, March 30, 2026 and Friday, May 1, 2026. There will be a comprehensive final exam on Wednesday, May 13, 2026.

Exams and solutions from previous semesters.

Spring 2020 Class exam 1
Spring 2020 Class exam 1: Solutions
Spring 2020 Class exam 2
Spring 2020 Class exam 2: Solutions
Spring 2020 Final exam
Spring 2020 Final exam: Solutions
Spring 2021 Class exam 1
Spring 2021 Class exam 1: Solutions
Spring 2021 Class exam 2
Spring 2021 Class exam 2: Solutions
Spring 2021 Class exam 3
Spring 2021 Class exam 3: Solutions
Spring 2021 Final exam
Spring 2021 Final exam: Solutions

Exams and solutions from this semester.

Solutions will be posted after each exam has been graded.

Spring 2026 Class exam 1
Spring 2026 Class exam 1: Solutions
Spring 2026 Class exam 2
Spring 2026 Class exam 2: Solutions
Spring 2026 Class exam 3
Spring 2026 Class exam 3: Solutions

Links and Animations

  1. Reference Sources
    1. Physlink. Reference information and data, including decimal system notation, physical constants, math constants, astro-physical constants, etc,....
    2. Eric Weinstein's World of Physics. Encyclopedia of Physics maintained by Wolfram Research. Entries at a variety of technical levels.
    3. Periodic Table of Elements. WebElements site.
    4. NIST Standard Reference Databases. Administered by the National Institute for Standards and Technology. The final word in physical data. Intended for professionals.
  2. Animations
    1. PhET. From the University of Colorado.
    2. oPhysics Physics simulations provided by Tom Walsh.
    3. LTU Applets. Collection of simulations provided by Scott Schneider, Lawrence Technological University.
    4. Animations for Physics and Astronomy. Collection of simulations from Dr. Michael R. Gallis, Penn State University, Schuylkill. Youtube channel
    5. Physclips. Collection of simulations from the University of New South Wales, Australia.
    6. The Quantum Mechanics Visualisation Project (QuVis). Collection of simulations from the University of St. Andrews, United Kingdom.
  3. General Quantum Theory
    1. Physic Magazine: IYQ Quantum Milestones APS article with highlights from the International Year of Quantum (2025).
    2. Physic Magazine: Quantum Physics APS magazine highlighting recent developments in physics.
  4. Historical Quantum Phenomena
    1. Hydrogen Atom Models From PhET, the University of Colorado.
    2. Molar Heat Capacity of Copper From Stevens and Boerio-Gates, J. Chem. Therm. vol 36, p 857 (2004).
    3. Blackbody Spectrum From PhET, the University of Colorado.
    4. Photoelectric Effect From PhET, the University of Colorado.
    5. Photomultiplier YouTube video from Ted Baldwin.
    6. Photomultiplier Tubes From Hamamatsu.
    7. Photomultiplier Tubes Handbook from Hamamatsu.
    8. A Direct Photoelectric Determination of Planck's "h", R. A. Millikan, Phys. Rev. 7, 355 (1916). Millikan's original article on the verification of Einstein's model of the photoelectric effect.
    9. Photon Absorption: Photoelectric Effect. From PSU Schuylkill.
    10. Coherent Scattering. From From PSU Schuylkill.
    11. X-ray Production. Youtube video from Succeed Technologies.
    12. X-ray Diffraction Patterns. From University of Pennsylvania.
    13. A Quantum Theory of the Scattering of X-rays by Light Elements, A. H. Compton, Phys. Rev. 21, 483 (1923). Compton's original article describing the Compton effect.
  5. Photon Phenomena
    1. Parametric Down Conversion Visualization From David Gorski.
  6. Photon Interference
    1. Photon Interference From QuVis, the University of St. Andrews.
    2. Quantum Wave Interference From PhET, the University of Colorado.
    3. Photon interference From Lyman Page, Princeton University.
  7. Particle Wave Phenomena
    1. Physics Web Excellent summary of experimental efforts to demonstrate interference and diffraction of particles passing through single and multiple slits. From Physics World.
    2. Rutherford Scattering From PhET, The University of Colorado.
    3. Electron interference patterns from Hitachi, Japan.
    4. Electron interference patterns from IMM Institute of the Italian National Research Council (CNR)
    5. Electron Scattering Davisson-Germer experiment. From PhET, The University of Colorado.
    6. Single Slit Diffraction of Neutrons, C. G. Shull, Phys. Rev. 179, 252 (1969). Description of a neutron single slit diffraction experiment.
    7. Single and Double Slit Diffraction of Neutrons, A. Zeilinger, R. Gahler, C. G. Shull, W Treimer, W Mampe, Rev. Mod. Phys. 60, 1067 (1988). Description of a neutron single and double slit diffraction experiments.
    8. Optics and interferometry with atoms and molecules, A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, Rev. Mod. Phys. 81, 1051 (2009). Overview of particle interference experiments.
    9. Colloquium: Quantum interference of clusters and molecules, K. Hornberger, et. al., Rev. Mod. Phys. 84, 157 (2012). Description of a particle interference experiments.
    10. Fullerene Diffraction From Anton Zeilinger, University of Innsbruck, Austria,
    11. Electron microscopy Assorted images from Wikipedia.
    12. Electron diffraction Images from NIH.
  8. Atomic spectra and atomic models
    1. Hydrogen Spectrum from McQuarrie and Simon.
    2. Models of the Hydrogen Atom From PhET, The University of Colorado.
  9. Probability
    1. Plinko Probability PhET, The University of Colorado.
  10. Uncertainty Principle
    1. O. Nairz, M. Arndt, and A. Zeilinger, "Experimental verification of the Heisenberg uncertainty principle for fullerene molecules," Phys. Rev. A 66, 032109 (2002). Demonstration of the uncertainty principle in large molecules.
  11. Bound states
    1. Quantum Bound States PhET, The University of Colorado.
    2. 1-d Quantum States From Paul Falstad.
    3. Trapped Ion Quantum Information University of Innsbruck.
    4. Trapped Ion Quantum Information Chris Monroe's group, Duke University.
    5. Quantum Dots From Nanohub. Tutorials and applications.
    6. Quantum Dots Available from CD Bioparticles. Describes applications.
    7. QNA Technology Sells quantum dots.
    8. Quantum Dots and Biomedical Assays From LBNL.
    9. Quantum Dots Available from CD Bioparticles. Describes applications.
    10. QNA Technology Sells quantum dots.
    11. Quantum Dots and Biomedical Assays From LBNL.
    12. Quantum Dot-Based Nanotools for Bioimaging, Diagnostics, and Drug Delivery, Regina Bilan, et.al., Chem. Biochem. 17, 2103 (2016).
    13. Quantum Dots in Diagnostics and Detection: Principles and Paradigms, T. R. Pisanic, et.al., Analyst 139, 2968, (2014).
    14. Quantum Dots in Diagnostics and Detection: Principles and Paradigms, T. R. Pisanic, et.al., Analyst 139, 2968, (2014).
  12. Oscillators
    1. Molecular Vibrations. From ChemTube3D.
    2. Normal Modes PhET, The University of Colorado.
    3. Quantum Optomechanics Aspelmeyer Group, University of Vienna.
    4. Molecular Vibrations from Edwin Scauble, University of California at Los Angeles.
    5. A. Gaidarzhy, G. Zolfagharkhani, R. L. Badzey, and P. Mohanty, "Evidence for Quantized Displacement in Macroscopic Nanomechanical Oscillators," Phys. Rev. Lett. 94 030402 (2005). Possibly the first experimental demonstration of quantum mechanical effects in a macroscopic oscillator - accomplished in 2005.
    6. F. Pistolesi, A. N. Cleland, and A. Bachtold, "Proposal for a Nanomechanical Qubit," Phys. Rev. X 11 031027 (2020). Possible use of a quantum harmonic oscillator for quantum information.
    7. Patricio Arrangoiz-Arriola, et.al. "Resolving the energy levels of a nanomechanical oscillator," Nature Phys. Rev. Lett. 571, 537-540 (2019). Appears to show the three lowest energy modes of a mechanical oscillator. arXiv article.
    8. Bjorn Schrinski, Yu Yang, Uwe von Lupke, Marius Bild, Yiwen Chu, Klaus Hornberger, Stefan Nimmrichter, and Matteo Fadel, "Macroscopic Quantum Test with Bulk Acoustic Wave Resonators," Phys. Rev. Lett. 130, 133604 (2023). Collection of a microgram of atoms oscillating.
  13. Tunneling
    1. Nobel Prize in Physics 2025. For macroscopic tunneling.
    2. Experimental Evidence for Quantum Tunneling Time, Nicolas Camus, et.al., Phys. Rev. Lett., 119, 023201 (2017).
    3. Scanning Tunneling Microscopy from nanoScience Instruments.
    4. Invention of STM from This Month in Physics History, August/September 2003.
    5. Scanning Probe Microscopy: From Sublime to Ubiquitous 30th anniversary collection from Physical Review Letters.
    6. 30 Years of Moving Atoms from Chemical and Engineering News.
    7. STM Quantum Made Simple.
    8. NaioSTM Table top STM.
    9. Surface studies with a scanning tunnelling microscope. YouTube video from MPI.
    10. A Boy and His Atom. Atomic stop frame movie, IBM.
  14. Spin
    1. Spin, Quantum Made Simple from Toutestquantique.
    2. Stern-Gerlach Experiment from QuantumVisions.