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Charlier Polynomials and Translational Invariance in the Quantum Harmonic Oscillator

✍ Scribed by Franciszek Hugon Szafraniec

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
151 KB
Volume
241
Category
Article
ISSN
0025-584X

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✦ Synopsis

In a recent paper the creation operator of the quantum harmonic oscillator (its counterpart, the annihilation one as well) is characterized through its (spatial) translational invariance property. Here we step up with replacing the operator theoretic reasoning of [5] by an orthogonal polynomial environment which let the arguments become natural. This settles the result well in the circumstances of (as well as those of ).

This surprising result was inspired by the uniqueness theorem of and that, in 2000

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