
Physics 2000
Unitary relation between a harmonic oscillator of timedependent frequency and a simple harmonic oscillator with and without an inversesquare potentialDOI: 10.1103/PhysRevA.62.014103 Abstract: The unitary operator which transforms a harmonic oscillator system of timedependent frequency into that of a simple harmonic oscillator of different timescale is found, with and without an inversesquare potential. It is shown that for both cases, this operator can be used in finding complete sets of wave functions of a generalized harmonic oscillator system from the wellknown sets of the simple harmonic oscillator. Exact invariants of the timedependent systems can also be obtained from the constant Hamiltonians of unit mass and frequency by making use of this unitary transformation. The geometric phases for the wave functions of a generalized harmonic oscillator with an inversesquare potential are given.
