Quantum mechanical sum rules for two model systems

Abstract

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.

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

References in corpus (4)

• QCD Sum Rules and Applications to Nuclear Physics
• The Evolution and Revival Structure of Localized Quantum Wave Packets
• More Conservation Laws and Sum Rules in the Heavy Quark Limit
• Conservation Laws and Sum Rules in the Heavy Quark Limit

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