Conformal Transformation of the Schrödinger Equation for the Harmonic Oscillator into a Simpler Form

2010/03/03 by Robert J. Ducharme, Ducharme, Robert J.
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph

paper · pdf · doi:10.48550/arxiv.1003.0717

7 pages

arxiv created 2010/03/03 · arxiv updated 2010/03/05

Abstract

The Schrödinger equation and ladder operators for the harmonic oscillator are shown to simplify through the use of an isometric conformal transformation. These results are discussed in relation to the Bargmann representation. It is further demonstrated that harmonic interactions can be introduced into quantum mechanics as an imaginary component of time equivalent to adding the oscillator potential into the hamiltonian for the confined particle.

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