Numerical solution of the two-dimensional time independent Schrödinger equation with Numerov-type methods

The solution of the two-dimensional time-independent Schrödinger equation is considered by partial discretization. The discretized problem is treated as an ordinary differential equation problem and Numerov type methods are used to solve it. Specifically the classical Numerov method, the exponentially and trigonometrically fitting modified Numerov methods of Vanden Berghe et al. [Int. J. Comp. Math 32 (1990) 233–242], and the minimum phase-lag method of Rao et al. [Int. J. Comp. Math 37 (1990) 63–77] are applied to this problem. All methods are applied for the computation of the eigenvalues of the two-dimensional harmonic oscillator and the two-dimensional Henon–Heils potential. The results are compared with the results produced by full discterization.