Conformal Transformation of the Schr'{o}dinger Equation for the Harmonic Oscillator into a Simpler Form

摘要

The Schr\"{o}dinger equation and ladder operators for the harmonic oscillatorare shown to simplify through the use of an isometric conformal transformation.These results are discussed in relation to the Bargmann representation. It isfurther demonstrated that harmonic interactions can be introduced into quantummechanics as an imaginary component of time equivalent to adding the oscillatorpotential into the hamiltonian for the confined particle.