Computation of the linear Schrodinger Energy levels by Sinc method

Subject Areas : Statistics

Kh.  Nouroozi ¹ (Department of mathematics, Qom University of technology, Qom, Iran)
S. M.A.  Aleomraninejad ² (Department of mathematics, Qom University of technology, Qom, Iran)
M.  Solaimani ³ (Department of physics, Qom University of technology, Qom, Iran)
B.  Farnam ⁴ (Department of mathematics, Qom University of technology, Qom, Iran)

Received: 2017-02-28 Accepted : 2017-07-06 Published : 2017-10-23

Keywords: روش هم محلی سینک, روش تفاضلات متناهی, مقدار ویژه, بردار ویژه,

Abstract :

Computation of the Schrodinger equation energy levels is very important in physics. For example we can use these levels to calculate the absorption coefficient and light refraction in a material as well as calculation of the interband and intersubband transition energies. Density of states of the system can also be obtained by using the energy levels. Thereafter we can determine that the system is dielectric, semiconductor or metal. There are different methods to calculate the energy levels and each of them has some advantages and some disadvantages. The asymptotic iteration method, genetic algorithm, numerov method, neural networks, transfer matrix method etc. are some of them. However calculation of the energy levels by using the Sinc method has less been studied. In this paper we consider the Sinc collocation method to calculate these energy levels. We approximate the unknown function by Sinc functions and convert the problem to the eigenvalue problem by collocation method. In sequel numerical examples are included to compare the accurately of our method with finite difference method. The results demonstrate the accuracy of our method to comparison the other methods. All computations were carried out using Maple on a personal.

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