| 一维定域近弹性势下薛定谔波动方程的严格解 |
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| 引用本文： | 刘克家. 一维定域近弹性势下薛定谔波动方程的严格解[J]. 贵州工业大学学报(自然科学版), 1996, 0(5) |
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| 作者姓名： | 刘克家 |
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| 作者单位： | 贵州工学院冶金系 |
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| 摘 要： | 本文以严格的数学推导，求解了一特定势能下的量子力学波动方程。得出了此二阶微分方程的本征函数和本征值量子能级，以级数法得出的方程解是一新的正交多项式。此势能模型既有“无限深势阱”模型的特点，也有“简谐势振动”模型的特征。此方程的解在一定的条件下能退化为这两个模型的解。以严格的数学推导，得出了这一方程可化为“斯特姆—刘维”型微分方程。这就证明了：该方程的本征函数是正交的和完备的。
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| 关 键 词： | 量子力学；薛定谔波动方程的解；量子能级 |
SOLUTION TO SCHROOINGER''''S EQUATION FOR LOCATED HARMONIC POTENTIAL |
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| Liu Kejia. SOLUTION TO SCHROOINGER''''S EQUATION FOR LOCATED HARMONIC POTENTIAL[J]. Journal of Guizhou University of Technology(Natural Science Edition), 1996, 0(5) |
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| Authors: | Liu Kejia |
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| Affiliation: | Guizhou institue of Technology |
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| Abstract: | A quantum Schrodinger's equation for square tangent functional potentialis exactly solved, anel both the eigenialue and eigenfunction, i. e. a new kind of polynomial, are obtained, by means of power-series solutions.. This model is similar toboth quantum oscillator and the square well model, and the physical meaning of themodel is also discussed.It is proved that the equation belongs to the sturm-Liouvilledifferential equation. It is verified, therefore, that the eigenfuctions are orthogonaland complete. |
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| Keywords: | Quantum Mechanics solution of the Schrodinger's equation quantumenergy level |
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