To provide a numerical simulation apparatus capable of executing a numerical simulation with high speed and precision by reducing computational complexity. A numerical simulation apparatus that executes a numerical simulation using a wave function which is a solution of a time dependent Schrödinger equation includes: a real time evolution calculation unit that calculates a second wave function while evolving the second wave function from an initial time in increments of a predetermined time period, the second wave function being obtained by applying a central difference approximation in a real-space finite-difference method to a first wave function expressed using a propagator, and being expressed using a Bessel function; and a calculation result storage unit that stores a calculation result of the second wave function obtained at each time by the time evolution calculation unit while evolving the second wave function in increments of the predetermined time period.