Current generations of graphics processing units have turned into highly
parallel devices with general computing capabilities. Thus, graphics processing
units may be utilized, for example, to solve time dependent partial
differential equations by the Fourier split operator method. In this
contribution, we demonstrate that graphics processing units are capable to
calculate fast Fourier transforms much more efficiently than traditional
central processing units. Thus, graphics processing units render efficient
implementations of the Fourier split operator method possible. Performance
gains of more than an order of magnitude as compared to implementations for
traditional central processing units are reached in the solution of the time
dependent Schr\"odinger equation and the time dependent Dirac equation
