Abstract
In this chapter we summarize the mathematical principles of quantum mechanics, using a more abstract mathematical formulation than before. Many of the relations which will be considered here have already been discussed in the preceding chapters in a more “physical” way and most have been proved in detail. Some of the explanations and proofs are supplemented or demonstrated once again in a more compact manner in additional exercises.
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References
The German name for trace, “Spur”, is often used in the literature.
We will encounter this situation in W. Greiner: Relativistic Quantum Mechanics, 3rd ed. (Springer, Berlin, Heidelberg 2000), where the Dirac spinor also turns out to have four components: two for the spin and two for the particle-antiparticle degrees of freedom.
E.G. Harris: A Pedestrian Approach to Quantum Field Theory (Wiley, New York 1972).
J. von Neumann: The Mathematical Foundations of Quantum Mechanics (Princeton, NJ 1955).
J.M. Jauch: Foundations of Quantum Mechanics (Addison-Wesley, Reading, MA 1968).
See W. Greiner, B. Müller: Quantum Mechanics — Symmetries, 2nd ed. (Springer, Berlin, Heidelberg 1994), especially the section on isotropy in time.
See the extensive presentation of perturbation theory in Chap. 11 and, e.g., in A.S. Davydov: Quantum Mechanics (Pergamon, Oxford 1965), Chap. VII; L.L Schiff: Quantum Mechanics, 3rd ed. (McGraw-Hill, New York 1968), Chap. 8; A. Messiah: Quantum Mechanics, Vol. II (North-Holland, Amsterdam 1965).
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© 2001 Springer-Verlag Berlin Heidelberg
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Greiner, W. (2001). The Formal Framework of Quantum Mechanics. In: Quantum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56826-8_16
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DOI: https://doi.org/10.1007/978-3-642-56826-8_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67458-0
Online ISBN: 978-3-642-56826-8
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