Ground and excited states of one-dimensional self-interacting nonlinear oscillators through time-dependent quantum mechanics

Abstract

Energy eigenvalues, probability densities, and x2r values (r = 1 to 6) of one-dimensional self-interacting nonlinear oscillators have been obtained by evolving the time-dependent Schrodinger equation in imaginary time, coupled with the minimization of energy expectation values. For excited states, the orthogonality constraint with lower states is maintained. Probability density plots for the ground and first three excited states are presented. A comparison of energy eigenvalues and probability densities plots is also made between oscillators with and without self-interaction