The evolution operator technique in solving the Schrodinger equation, and its application to disentangling exponential operators and solving the problem of a mass-varying harmonic oscillator

Abstract

The authors present a method for finding the evolution operator for the Schrodinger equation for the Hamiltonian expressible as H(t)=a1(t)J4+a2(t)J0+a3(t) J- where J+, J0 and J- are the SU(2) group generators. Such a method is applied to the disentangling technique for exponential operators which are not necessarily unitary. As a demonstration of our general approach, they solved the problem of a harmonic oscillator with a varying mass.