Study on electronic bound states in multiple-well potential and formation of energy band

doi:10.3969/j.issn.1007-5461.2021.03.007

Abstract

Abstract: The energy levels and quantum states of electron in N symmetric potential well are investigated by using classical method. Based on Schr¨odinger equation and the standard conditions of wave function, the (4N − 2)-variables linear equations with undetermined coefficients in the wave function are derived. The transcendental equation is obtained from that the coefficient determinant equals to zero. Then the energy levels of electron are calculated by solving the transcendental equation, and the bound state wave function is obtained by calculating the basic solution set of the linear equations. In the case of N = 2 ∼ 5, well width of 1 nm and well spacing of 0.5 nm, the energy levels and wave functions are calculated numerically by using Mathematica software and the mechanism of the energy level splitting into energy band is exhibited intuitively. It is shown that the physical concept of the proposed method is clear, the process is simple and easy to understand, and in addition, there are no artificially adjusted parameters, and the calculation accuracy is high and the speed is fast.

Key words: quantum physics, energy level and wave function, linear equations, quantum well, numerical calculation, energy band

CLC Number:

O413.1

JIANG Junqin∗, TU Jing. Study on electronic bound states in multiple-well potential and formation of energy band[J]. Chinese Journal of Quantum Electronics, 2021, 38(3): 316-326.

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