The Lie algebraic solution of a time-dependent Schrodinger equation invariant under the algebra {sl(2, R),W} A1

摘要

Time-dependent quadratic Hamiltonians have diverse applications.We construct such a Hamiltonian from a representation of the elements of the algebra sl(2, R) W with each element having an independent, time-dependent coefficient.We demonstrate that the corresponding Schrodinger equation possesses the Lie algebra {sl (2, R) W}A1 and show how to construct the wave functions using this representation.