Quantum mechanical sum rules for two model systems

Details Quantum mechanical sum rules for two model systems Quantum mechanical sum rules for two model systems

2008-02-15

arxiv.org/abs/0802.2217v1

Physics

Quantum Physics

23 pages, no figures, to appear in Am. J. Phys

Scientific paper

10.1119/1.2908194

Sum rules have played an important role in the development of many branches of physics since the earliest days of quantum mechanics. We present examples of one-dimensional quantum mechanical sum rules and apply them in two familiar systems, the infinite well and the single delta-function potential. These cases illustrate the different ways in which such sum rules can be realized, and the varying mathematical techniques by which they can be confirmed. Using the same methods, we also evaluate the second-order energy shifts arising from the introduction of a constant external field, namely the Stark effect.

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