Computation of the eigenvalues of the Schrödinger equation by symplectic and trigonometrically fitted symplectic partitioned Runge–Kutta methods

In this Letter we present an explicit symplectic method for the numerical solution of the Schrödinger equation. We also develop a modified symplectic integrator with the trigonometrically fitted property based on this method. Our new methods are tested on the computation of the eigenvalues of the one-dimensional harmonic oscillator, the doubly anharmonic oscillator and the Morse potential.