New Method of Determining the Landau Levels in Narrow-Gap Semiconductors

Abstract

With the help of mathematical models, the temperature dependence of the density of energy states was determined in a quantizing magnetic field. The influence of the effective mass at the temperature dependence of the density of the energy states in a strong quantizing magnetic field is investigated. The dependence temperature of density of energy states graph is obtained in a strong magnetic field for InSb.

Solving Schrödinger Wave Equation for the Charmonium Spectrum Using Artificial Neural Networks

“…Numerov's matrix method [6], shooting method [7], and Crank-Nicolson's approach [8] are the numerical methods to solve the Schrödinger wave equation. Artificial neural networks, which were introduced in the field of high-energy physics in 1988 [9], can handle the increase in the complexity of data in physics processes, as reviewed in [10].…”

Unraveling the effects of non-parabolicity on electron energy levels in InP/InAs/InP heterostructures

“…The confinement of electrons and holes in potential wells results in the quantization of energy levels, which can be obtained by solving the Schrödinger equation [1][2][3]. Several approaches have been employed to solve this equation, including graphical methods [15][16][17], and various approximate techniques [18][19][20][21][22][23][24][25][26][27][28][29] numerical solutions [30][31][32][33][34].…”

“…For instance, Alharbi [31] utilized the finite difference method to investigate the effects of nonparabolicity on the energy states in quantum wells. Harrison [32] and Gulyamov et al [33,34] employed the shooting method to calculate the energy levels and wave functions in nanowires and quantum wells. Barsan and Ciornei [28] provided approximate analytical results for semiconductor quantum wells considering the BenDaniel-Duke boundary conditions.…”

“…Our approach seeks to strike a balance between the simplicity of the EMA and the need for accurate descriptions of electron behavior in the InP/InAs/InP heterostructure. Indeed, To address these limitations, our study employs Nelson's formula [36][37][38][39], the shooting method [32][33][34], and Garrett's formula [22] to correct the EMA and improve its accuracy in describing the electron behavior in the InP/InAs/InP heterostructure. By incorporating these corrections the authors try to provide a more realistic and reliable description of the electron energy levels in the presence of non-parabolicity and effective mass discontinuity.…”