*Quantum Mechanics and Path Integrals* — Solutions to Exercises V0.5
Progress on the exercise solutions continues to be slow going. The current version is 0.5, and compared with V0.4 it skips Chapters 8 and 9, tackling instead the exercises from the statistical mechanics material in Chapters 10 and 11.
Chapter 10 has 10 exercises, and Chapter 11 actually has none at all. That might sound like a light load, but every single one of these problems is genuinely hard. The main content of these two chapters is about using the path integral method to compute the partition function in statistical mechanics — which is already a fairly demanding topic in its own right. On top of that, Feynman's vivid but informal style of exposition in the book makes it easy to grasp the general picture, yet quite hard to actually carry the calculations through to the end. In fact, for the exercises in this chapter I had to consult a considerable amount of material, both in Chinese and in English, before I could get through them, however roughly.
Though I say "got through them," of course, in truth I only managed 9 out of the 10 problems. Problem 10-3 in particular left me puzzled: the result I obtained doesn't match the one Feynman gives, and I couldn't push the calculation any further. I'm raising it here in the hope that readers who understand the issue can enlighten me.
One more note: although Chapter 11, on the variational method, has no exercises of its own, its main calculations (such as computing the first-order path integral) are actually already embedded in the explanations and exercises of Chapter 10. So it's only by thoroughly understanding Chapter 10 that one can properly read Chapter 11. Incidentally, I think my own earlier (admittedly clumsy) piece, The Extremal Principle for Score Estimation — A Beginner's Version of the Variational Principle, is quite helpful for anyone just starting to learn the variational principle.
Download: Quantum Mechanics and Path Integrals — Solutions to Exercises V0.5.pdf
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