Numerical approach by quasi-spectral and fitting methods to study Schrodinger equation and calculating the energy levels of flat potentials

Abstract

In this paper, flat potentials (μ│x / a│N) are numerically investigated by pseudo-spectral method. The Schrodinger equation of this type of potential has become an eigen system using the pseudo-spectral method. The eigen system is then diagonalized by the Jacobi method. Energy eigen values for different Ns have been compared with similar articles. The limit behavior of this potential for the states N = 2 and N → ∞ is related to the harmonic oscillator and the particle in the box with length 2a, respectively. For each N, a function is proposed for energy eigen values in terms of the quantum number n. By using of data fitting, the correctness of the proposed equation is checked.