HAMILTONIAN OF THE ONE-DIMENSIONAL TORSION SCHRODINGER EQUATION IN A COMPLEX-VALUED BASIS OF MATHIEU FUNCTIONS

被引：1
|
作者：
Belov, A. N. [1 ]
Turovtsev, V. V. [2 ]
Orlov, Yu. D. [1 ]
机构：
[1] Tver State Univ, Tver, Russia
[2] Tver State Med Univ, Tver, Russia
来源：
RUSSIAN PHYSICS JOURNAL | 2017年 / 60卷 / 06期
关键词：
Schrodinger equation; Mathieu functions; torsion equation;
D O I：
10.1007/s11182-017-1160-1
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
An analytical method for calculating the matrix elements of the Hamiltonian of the torsion Schrodinger equation in a basis of Mathieu functions is developed. The matrix elements are represented by integrals of the product of three Mathieu functions, and also the derivatives of these functions. Analytical expressions for the matrix elements are obtained by approximating the Mathieu functions by Fourier series and are products of the corresponding Fourier expansion coefficients. It is shown that replacing high-order Mathieu functions by one harmonic leads to insignificant errors in the calculation.
引用
收藏
页码：928 / 934
页数：7
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