98-277 George A. Hagedorn
Raising and Lowering Operators for Semiclassical Wave Packets (906K, uuencoded gzipped postscript) Apr 19, 98
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Abstract. We construct raising and lowering operators for certain orthonormal bases of $L^2(\zR^n)$. These bases consist of quantum mechanical wave packets that can be used to develop asymptotic expansions for solutions to the time--dependent Schr\"odinger equation in the semiclassical limit. With the knowledge of the raising and lowering operators, we simplify the construction of these bases and the proofs of their crucial properties. We also present simplified proofs of several results in semiclassical quantum mechanics.

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