- 98-277 George A. Hagedorn
- Raising and Lowering Operators for Semiclassical Wave Packets
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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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