Closed form solution for a double quantum well using Gr?bner basis

Acus A.; Dargys A.

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Closed form solution for a double quantum well using Gr?bner basis

机译：使用Gr？bner基的双量子阱的封闭形式解

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Analytical expressions for the spectrum, eigenfunctions and dipole matrix elements of a square double quantum well (DQW) are presented for a general case when the potential in different regions of the DQW has different heights and the effective masses are different. This was achieved by using a Gr?bner basis algorithm that allowed us to disentangle the resulting coupled polynomials without explicitly solving the transcendental eigenvalue equation.

机译：在一般情况下，当DQW的不同区域中的电势具有不同的高度且有效质量不同时，将给出正方形双量子阱（DQW）的光谱，本征函数和偶极矩阵元素的解析表达式。这是通过使用Gr？bner基算法实现的，该算法允许我们在不显式求解先验特征值方程的情况下解开生成的耦合多项式。

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《Physica Scripta: An International Journal for Experimental and Theoretical Physics》 |2011年第1期|共5页
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Acus A.; Dargys A.;
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1. Closed form solution for a double quantum well using Gr?bner basis [J] . Acus A., Dargys A. Physica Scripta: An International Journal for Experimental and Theoretical Physics . 2011,第1期

机译：使用Gr？bner基的双量子阱的封闭形式解
2. Gr?bner-Shirshov basis of quantum group of type E_6 [J] . Obul A., Yunus G. Journal of Algebra . 2011,第1期

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3. Gr(o)bner-Shirshov Basis of Quantum Group of Type D4 [J] . Gulshadam YUNUS, Abdukadir OBUL 数学年刊B辑（英文版） . 2011,第004期

机译：D4型量子群的Gr（o）bner-Shirshov基础
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7. Gröbner–Shirshov basis of quantum group of type E6 [O] . Obul Abdukadir, Yunus Gulshadam 2011

机译：E6型量子群的Gröbner–Shirshov基础
8. Coupled Cluster Single and Double Excitation (CCSD) Method in Quantum Chemistry: An Efficient Formulation of the Theory and Application to Closed Shell Molecular Systems [R] . Scheiner, A. C. 1987

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Closed form solution for a double quantum well using Gr?bner basis

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