New Second-order Exponentially and Trigonometrically Fitted Symplectic Integrators for the Numerical Solution of the Time-independent Schr?dinger Equation

摘要

The solution of the one-dimensional time-independent Schr?dinger equation is considered by trigonometrically and exponentially fitted symplectic integrators. The Schr?dinger equation is first transformed into a Hamiltonian canonical equation. Numerical results are obtained for the one-dimensional harmonic oscillator, doubly anharmonic oscillator and the exponential potential.