This file is Transition to Quantum.doc, version 16 January 2008. These notes for Quantum Physics PHY 571 (Venables) are only intended as a summary, and to give references. They do not contain all the arguments. References are to the textbooks Gasiorowicz (G3 or G2 for the two editions) and Liboff (L4 or L3). Of course only one of these references is needed in general. 1. Postulates of Quantum Mechanics (refs G3 p23-42, chapter 3 read through, runs into chapters 5 and 6; G2 p27-53, read through and runs into chapter 4, 6-7; L4 chapter 3, p69 onwards, L3 chapter 3, p69 onwards). Griffiths starts with the postulates in chapter 1, and is all done by page 5; but then of course he has to backtrack and goes into a section on probability. I am assuming that you have already had this topic in another course, sometime, somewhere. There are several ideas contained in the postulates, such as the idea of the wavefunction, the form of the Schrödinger Equation, the probability interpretation, the role of measurement, and wavefunction collapse onto an eigenstate (following a measurement). These are all treated in different order and in different ways in the various books; for example the last topic is named ‘the expansion postulate and its physical interpretation’ in Gasiorowicz; refs for this last topic are G3, p53-55, G2, 60-62, L4 p76, L3, p75, and Griffiths p 3-5; essentially, there is not widespread agreement about the order to teach/ learn this stuff, nor on how much weight to give to each topic. 2. Introduction to the Schrödinger Equation. Gasiorowicz starts for the SE for a free particle (V = 0) and ends up with summary page (ref G2 p51) that I have handed out in class. This discussion starts from G3 eqn 2.22, page 31, or G2 eqn 3.1, p 41). In the derivation I did in class, I gave equation numbers to both G3 and G2, so you can check back with the books. We explored the derivation of the probability current (refs G3 p 35, G2, p45, or L4, p 216-219, L3 p 224-227), and ideas of conservation of particles. We then did the example of an electron traversing a thin film, as in an electron microscope, and the theorem that probability current is not conserved in the presence of a complex potential. G3 has this as a problem (#11, p42) but G2 spells this out on p44-45. Keeping our aim of understanding the summary page, we discussed the role of operators, commutation relations, Poisson Brackets, and representations. The role of position (x) and momentum (p) representations were emphasized, and the non-zero value of the PB for conjugate variables, which do not commute, to the Uncertainty Principle was emphasized. 3. Eigenvalue problems (refs Handouts of web pages, either the current versions with references to G3 and L4, or the older (2001-03) version with refs to G2 and L3). The main points are: a) to remember and apply the expansion postulate; b) to do some of these problems, get a good feel for the underlying physics; c) to study past Comps Problems if you need to; d) Not to spend the entire semester on such problems, as there are a lot of them.
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