Schwinger J. Quantum mechanics. Symbolism of atomic measurement
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Springer, 2001, 498 p. The lecture notes of Schwinger's UCLA course consist of three parts corresponding to the three quarters of teaching. Here is a brief summary of the contents. Part A, the material of the fall quarter, begins with an analysis of experiments of the Stern-Gerlach type that accomplishes "a self-contained physical and mathematical development of the general structure of quantum kinematics" . Much technical material is delivered in passing. In particular, unitary transformations are studied from various angles, and the algebra of angular momentum is treated in depth. Then, an analysis of Galilean invariance yields the non-relativistic Hamilton operator. The winter quarter, Part B, proceeds from there. The response to infinitesimal time displacements establishes the equations of motion. Then the Quantum Action Principle is derived, and accepted as a fundamental principle. In a sense, the rest of Part B and all of Part C consist of instructive applications of the action principle - the "numerous examples" referred to above. Part B contains treatments of, among others, the (driven) harmonic oscillator, bound-state properties of hydrogenic atoms, and Rutherford scattering. Part C (spring quarter) begins with the two-particle Coulomb problem, including the modifications for two identical particles. The treatment of systems with many identical particles follows, where the notion of second quantization eventually leads to the concept of the quantized field. As a first application, the Hartree-Fock and Thomas-Fermi approaches to many-electron atoms are presented, the latter in considerable detail. The second and final application is the quantum theory of electromagnetic radiation, which is developed to the extent necessary for an understanding of (the non-relativistic aspects of) the Lamb shift.
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