![schrödinger model schrödinger model](http://image.slidesharecdn.com/tang02-schrdingersatomicmodel-120926183019-phpapp02/95/tang-02-schrdingers-atomic-model-3-728.jpg)
The specific form of wave function and corresponding energy can be obtained by solving this equation, so as to understand the properties of microsystem. Indeed, each microsystem has a corresponding Schrodinger equation. Known to all, the standard Schrödinger equation is a second-order partial differential equation established by combining the concept of matter wave and wave equation, and it can describe the movement of microparticles. Schrödinger equation, being known as basic assumption of quantum mechanics, is one of the most important equations in quantum mechanics that proposed by Austrian physicist Schrödinger. Finally, several numerical examples are presented to support our analysis.
![schrödinger model schrödinger model](https://img.haikudeck.com/mg/EC0304C4-5E66-47AD-B200-CB104076CAE1.jpg)
The error of the semidiscrete Fourier spectral scheme is analyzed in the proper Sobolev space.
![schrödinger model schrödinger model](http://cahistoryofatom.weebly.com/uploads/2/1/6/1/21614116/header_images/1378155049.jpg)
The proof of the conservation law of the mass and the energy for the semidiscrete and full-discrete Fourier spectral scheme is given. The Fourier spectral method is applied to approximate the spatial direction, and fourth order exponential time-differencing Runge-Kutta method is used to discrete temporal direction. In this paper, Fourier spectral method combined with modified fourth order exponential time-differencing Runge-Kutta is proposed to solve the nonlinear Schrödinger equation with a source term.