Chapter 3 Further Reading

Primary Textbook References

Griffiths & Schroeter, Introduction to Quantum Mechanics, 3rd ed. (Cambridge, 2018)

  • Chapter 2: Time-independent Schrödinger equation. Covers the infinite well (§2.2), harmonic oscillator (§2.3), free particle (§2.4), delta-function potential (§2.5), and finite square well (§2.6). This is the standard reference and our primary parallel text. Griffiths' treatment of the infinite well and tunneling is particularly clear.
  • Chapter 2, §2.5: The delta-function potential — not covered in our Chapter 3 but an elegant limiting case of the finite well (see Exercise 3.14). Short and illuminating.

Shankar, Principles of Quantum Mechanics, 2nd ed. (Springer, 1994)

  • Chapter 5: Simple problems in one dimension. Shankar's treatment is more mathematically rigorous than Griffiths and provides deeper discussion of the free particle and wave packets. His derivation of the tunneling formula is particularly thorough.
  • §5.4: Tunneling with detailed treatment of the transfer matrix method — a systematic approach to layered potentials that generalizes beyond rectangular barriers.

Sakurai & Napolitano, Modern Quantum Mechanics, 3rd ed. (Cambridge, 2021)

  • Chapter 2, §2.5: Free particle propagator and wave packet dynamics in the Heisenberg picture. More advanced but gives important perspective on the time evolution we computed in §3.3.

Cohen-Tannoudji, Diu & Laloë, Quantum Mechanics, Vols. 1 & 2 (Wiley, 2020)

  • Complement H_I: Square potentials — an encyclopedic treatment with every variant (step, well, barrier) worked out in full detail with probability currents. Excellent for those who want every last formula.

Supplementary Reading

On the Infinite Square Well and Exactly Solvable Problems

  • Robinett, R.W. "Quantum mechanics of the particle-in-a-box: dynamics and surprises." Am. J. Phys. 63, 823–832 (1995). An in-depth exploration of wave packet dynamics in the infinite well, including revival and fractional revival phenomena — the particle returns to its initial state after a specific time.

  • Styer, D.F. "The motion of wave packets through their expectation values and uncertainties." Am. J. Phys. 58, 742–744 (1990). Beautiful analysis of how expectation values and uncertainties behave in the infinite well.

On Quantum Tunneling

  • Merzbacher, E. "The early history of quantum tunneling." Physics Today 55(8), 44–49 (2002). An accessible historical account of how Gamow, Condon, and Gurney explained alpha decay via tunneling — one of the great early triumphs of quantum mechanics.

  • Razavy, M. Quantum Theory of Tunneling, 2nd ed. (World Scientific, 2014). A monograph devoted entirely to tunneling. Comprehensive treatment of rectangular barriers, WKB, multi-barrier systems, and dissipative tunneling. Advanced, but the first few chapters are accessible after this chapter.

  • Binnig, G. & Rohrer, H. "Scanning tunneling microscopy." Helv. Phys. Acta 55, 726–735 (1982). The original STM paper. Remarkably readable and short.

  • Binnig, G. & Rohrer, H. "Scanning tunneling microscopy — from birth to adolescence." Rev. Mod. Phys. 59, 615–625 (1987). Nobel lecture. Provides the physics behind STM with beautiful images and accessible explanations.

On Quantum Dots

  • Brus, L.E. "Electron–electron and electron–hole interactions in small semiconductor crystallites: The size dependence of the lowest excited electronic state." J. Chem. Phys. 80, 4403–4409 (1984). The paper where the Brus equation first appeared. Derives the size-dependent band gap from first principles.

  • Alivisatos, A.P. "Semiconductor clusters, nanocrystals, and quantum dots." Science 271, 933–937 (1996). Excellent review article connecting the physics of quantum confinement to materials science and applications.

  • Murray, C.B., Norris, D.J., & Bawendi, M.G. "Synthesis and characterization of nearly monodisperse CdE (E = sulfur, selenium, tellurium) semiconductor nanocrystallites." J. Am. Chem. Soc. 115, 8706–8715 (1993). The foundational synthesis paper that made high-quality quantum dots practical.

On Numerical Methods

  • Pillai, M., Goglio, J., & Walker, T.G. "Matrix numerov method for solving Schrödinger's equation." Am. J. Phys. 80, 1017–1019 (2012). A more accurate finite difference scheme (fourth-order rather than second-order) that is only slightly more complex to implement.

  • Press, W.H., Teukolsky, S.A., Vetterling, W.T., & Flannery, B.P. Numerical Recipes, 3rd ed. (Cambridge, 2007). Chapter 18 covers eigenvalue problems for ODEs, including the shooting method. Chapter 11 covers matrix eigenvalue methods. The gold standard reference for computational physics.

Video Lectures

  • MIT OpenCourseWare 8.04 (Allan Adams, 2016): Lectures 6–9 cover the infinite well, free particle, and tunneling with exceptional clarity and enthusiasm. Freely available on YouTube.

  • Feynman Lectures on Physics, Vol. III, Chapters 6–7: Feynman's treatment of the double-well and ammonia molecule is unmatched for physical insight, though the notation differs from ours.

Historical Sources

  • Schrödinger, E. "Quantisierung als Eigenwertproblem" (Quantization as an eigenvalue problem). Ann. Phys. 79, 361–376 (1926). The original paper where Schrödinger solved the hydrogen atom using his wave equation. Available in English translation.

  • Gamow, G. "Zur Quantentheorie des Atomkernes" (On the quantum theory of the atomic nucleus). Z. Phys. 51, 204–212 (1928). Gamow's alpha decay tunneling paper — the first application of tunneling to nuclear physics.

Online Resources

  • Paul Falstad's Quantum Mechanics Applets (https://falstad.com/qm1d/): Interactive 1D Schrödinger equation solver. Excellent for building intuition by changing potentials and watching eigenstates respond in real time.

  • PhET Simulations — Quantum Tunneling and Wave Packets (https://phet.colorado.edu/): Free interactive simulation from the University of Colorado. Allows you to adjust barrier height, width, and particle energy and see the transmitted and reflected components.

If you found the infinite well most interesting → Griffiths §2.2 for more details, then jump to Chapter 4 (harmonic oscillator) for the next exactly solvable problem.

If you found tunneling most interesting → Merzbacher's Physics Today article for history, Razavy's monograph for comprehensive theory, then look ahead to Chapter 20 (WKB approximation) for the generalization to arbitrary barriers.

If you found numerical methods most interesting → Pillai et al. for a better finite-difference scheme, Press et al. for industrial-strength algorithms, then explore the code in code/project-checkpoint.py and try it on new potentials.