Chapter 21 Further Reading

Primary Textbook References

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

  • Chapter 11.1–11.2: Time-dependent perturbation theory and the interaction picture. Griffiths' treatment is characteristically clear, with the two-level system as the central example. His comparison of perturbation theory with the exact Rabi solution (Section 11.2.3) is particularly helpful for understanding the domain of validity.
  • Chapter 11.3: Emission and absorption of radiation. The derivation of Einstein's A and B coefficients is presented with Griffiths' trademark pedagogical care. His treatment of selection rules via the Wigner-Eckart theorem is more streamlined than ours — worth comparing.

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

  • Chapter 5.6–5.8: Time-dependent perturbation theory. Sakurai's approach emphasizes the interaction picture from the outset and derives the Dyson series to all orders before specializing to first order. Section 5.7 on the application to electromagnetic interactions is the gold standard — rigorous, elegant, and physically transparent.
  • Chapter 5.8: Photoelectric effect derived from Fermi's golden rule. A beautiful application showing how quantum mechanics explains the phenomenon that launched the quantum revolution (Chapter 1 of our book).

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

  • Chapter 18: Time-dependent perturbation theory. Shankar's treatment includes a particularly clear discussion of the "energy-time uncertainty relation" emerging from the $\sin^2$ transition probability. His Section 18.4 on the electromagnetic interaction uses SI units throughout, which some students find more comfortable.

Specialized References

Time-Dependent Perturbation Theory

  • Merzbacher, Quantum Mechanics (3rd ed., 1998), Chapters 19–20: A thorough and rigorous treatment that carries the perturbative expansion to second order and discusses many-body applications. Chapter 20 on the photon field provides an excellent bridge to the quantum optics treatment of spontaneous emission.
  • Cohen-Tannoudji, Diu, & Laloe, Quantum Mechanics (1977), Volume II, Chapter XIII: The French school's masterful treatment includes the most complete discussion of the density of states and the conditions of validity of Fermi's golden rule available at the textbook level. The "complements" sections contain 15 worked applications, each a mini-paper.
  • Baym, G., Lectures on Quantum Mechanics (1969, reprinted 2018), Chapter 13: A compact and physically motivated treatment that emphasizes the connection between time-dependent perturbation theory and scattering. Baym's derivation of the golden rule is a model of clarity.

Einstein Coefficients and Radiation Theory

  • Einstein, A., "Zur Quantentheorie der Strahlung," Physikalische Zeitschrift 18, 121–128 (1917): The original paper introducing the A and B coefficients. Available in English translation in van der Waerden, Sources of Quantum Mechanics (Dover, 1967). Remarkably readable — Einstein's argument is as clear today as it was a century ago.
  • Dirac, P. A. M., "The Quantum Theory of the Emission and Absorption of Radiation," Proceedings of the Royal Society A 114, 243–265 (1927): The paper that gave the first quantum-mechanical derivation of transition probabilities and introduced the interaction picture. This is where time-dependent perturbation theory was born.
  • Hilborn, R. C., "Einstein coefficients, cross sections, f values, dipole moments, and all that," American Journal of Physics 50, 982–986 (1982); erratum 51, 471 (1983): An invaluable reference that collects all the various ways of expressing transition rates (A, B, oscillator strength, cross section, etc.) and the conversion factors between them. Every spectroscopist should have this paper within arm's reach.

Selection Rules and Atomic Spectroscopy

  • Condon, E. U. & Shortley, G. H., The Theory of Atomic Spectra (Cambridge, 1935; reprinted 1991): The bible of atomic spectroscopy. Still the definitive reference for selection rules in multi-electron atoms, angular momentum coupling schemes, and line strengths. Dense but authoritative.
  • Sobel'man, I. I., Vainshtein, L. A., & Yukov, E. A., Excitation of Atoms and Broadening of Spectral Lines (Springer, 1995): A comprehensive treatment of radiative transitions including higher-multipole (M1, E2) processes, line broadening mechanisms, and collisional effects. More advanced but extremely useful for research applications.

Lasers and Quantum Electronics

  • Siegman, A. E., Lasers (University Science Books, 1986): The definitive textbook on laser physics. Comprehensive (over 1,000 pages) and beautifully written. Chapters 1–7 cover the quantum mechanics of stimulated emission, rate equations, gain, and cavity modes. An indispensable reference for anyone working with lasers.
  • Svelto, O., Principles of Lasers (5th ed., Springer, 2010): A more compact alternative to Siegman, widely used in graduate courses. Excellent treatment of specific laser systems (gas, solid-state, semiconductor, fiber).
  • Milonni, P. W. & Eberly, J. H., Laser Physics (2nd ed., Wiley, 2010): A modern treatment that integrates the quantum mechanics (including a clear derivation of the Schawlow-Townes linewidth) with practical laser engineering. Particularly good on pulsed lasers and ultrafast optics.
  • Maiman, T. H., "Stimulated Optical Radiation in Ruby," Nature 187, 493–494 (1960): A one-page paper announcing the first laser. Its brevity belies its enormous impact. Compare with the much longer theoretical paper by Schawlow and Townes that predicted the laser ("Infrared and Optical Masers," Physical Review 112, 1940 (1958)).

Spontaneous Emission: The Quantum Field Theory Perspective

  • Milonni, P. W., "Why spontaneous emission?" American Journal of Physics 52, 340–343 (1984): A thought-provoking discussion of whether spontaneous emission is "caused by" vacuum fluctuations or radiation reaction — or whether the distinction is gauge-dependent and therefore unphysical.
  • Dalibard, J., Dupont-Roc, J., & Cohen-Tannoudji, C., "Vacuum fluctuations and radiation reaction: identification of their respective contributions," Journal de Physique 43, 1617–1638 (1982): The definitive resolution of the vacuum fluctuations vs. radiation reaction debate. Shows that in symmetric ordering, vacuum fluctuations and radiation reaction each contribute exactly half the spontaneous emission rate.

Historical and Conceptual

  • Pais, A., "Subtle is the Lord..." The Science and the Life of Albert Einstein (Oxford, 1982): Chapter 21 provides a masterful account of Einstein's 1917 radiation paper, placing it in the context of the old quantum theory and the road to quantum mechanics.
  • Bertolotti, M., The History of the Laser (CRC Press, 2004): A comprehensive history from Einstein's 1917 prediction of stimulated emission through the "laser wars" (the priority disputes between Townes, Schawlow, Gould, and Maiman) to modern applications. Fascinating reading for anyone interested in how physics becomes technology.
  • Hecht, J., Beam: The Race to Make the Laser (Oxford, 2005): A more accessible and narrative-driven account of the same history, emphasizing the human drama of the invention of the laser.

Computational

  • Johansson, J. R., Nation, P. D., & Nori, F., "QuTiP 2: A Python framework for the dynamics of open quantum systems," Computer Physics Communications 184, 1234 (2013): The QuTiP library provides mesolve() for time-dependent master equations, which can be used to compute transition probabilities beyond first-order perturbation theory. The documentation includes tutorials on driven two-level systems and spontaneous emission in open quantum systems.
  • Steck, D. A., Quantum and Atom Optics (free online textbook, steck.us/teaching, updated regularly): Chapters 1–5 cover the semiclassical atom-field interaction, Einstein coefficients, and the optical Bloch equations with a modern perspective and detailed calculations. Chapter 7 covers the quantized field approach to spontaneous emission. A superb free resource.

For the Adventurous

  • Purcell, E. M., "Spontaneous emission probabilities at radio frequencies," Physical Review 69, 681 (1946): A brief abstract (10 lines!) that predicted the modification of spontaneous emission rates by cavity environments — the Purcell effect. This paper launched the field of cavity QED and is a beautiful example of how a simple dimensional argument can predict deep physics.
  • Haroche, S. & Raimond, J.-M., Exploring the Quantum: Atoms, Cavities, and Photons (Oxford, 2006): A Nobel Prize-winning treatment of cavity QED — what happens when you put atoms inside cavities and control spontaneous emission at the single-photon level. Chapters 4–6 build directly on the Einstein coefficients and Fermi's golden rule developed in this chapter.
  • Lamb, W. E., Jr., "Anti-photon," Applied Physics B 60, 77–84 (1995): A provocative essay by the co-discoverer of the Lamb shift, arguing that the "photon" concept is more trouble than it is worth in most contexts and that semiclassical radiation theory suffices for everything except certain quantum optics experiments. A useful corrective to the naive overuse of particle language.