Obtaining the Higher Excited States in Two Dimensions Using the Finite Difference Time Domain Method

In this paper, we present a new numerical procedure using the finite difference time domain method (FDTD) to obtain the higher radial excited state wave functions of two-dimensional potentials. Their corresponding energy eigenvalues are also calculated. This procedure is based on an improvement of the iterative process of the initial guess wave function to force it to lead to any desired excited states rather than the ground state. In this improved method the even and the odd excited states are calculated separately by classifying the initial guess wave function using the symmetric properties to even (odd) parity wave functions that contain even (odd) numbers of lines of zeros. This technique is illustrated by applying it to a two dimensional symmetric harmonic oscillator.