| 角动量算符的矢积与标积的并矢计算和它的应用 |
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| 引用本文： | 赵汝顺.角动量算符的矢积与标积的并矢计算和它的应用[J].辽宁师范大学学报(自然科学版),2006,29(1):34-36. |
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| 作者姓名： | 赵汝顺 |
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| 作者单位： | 鞍山科技大学,理学院,辽宁,鞍山,114044 |
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| 摘 要： | 在量子力学中求解球对称辏力场中的薛定锷方程时，角动量算符的几个代表关系起着关键作用．笔者利用矢量算符的并矢计算的方法，对在量子力学中常用到的角动最算符的矢积与标积的公式,给出了一个不依赖于角动量算符的坐标表示的推导，并将它们应用于推导薛定锷方程的球坐标表示，角动量算符的矢量积公式实际上就是角动量算符之间的对易关系．最后我们将对易关系、经典泊松括号与矢量积三者作了一个有趣的对比，得出了这三者所具有的共同性质：反对易性和Jacohi恒等式．
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| 关 键 词： | 角动量算符 并矢 薛定锷方程 |
| 文章编号： | 1000-1735(2006)01-0034-03 |
| 收稿时间： | 11 13 2005 12:00AM |
| 修稿时间： | 2005年11月13 |
A Dyadic Calculation of the Vector and Scalar Products of Two Angular Momentum Operators in Quantum Mechanics |
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| ZHAO Ru-shun.A Dyadic Calculation of the Vector and Scalar Products of Two Angular Momentum Operators in Quantum Mechanics[J].Journal of Liaoning Normal University(Natural Science Edition),2006,29(1):34-36. |
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| Authors: | ZHAO Ru-shun |
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| Institution: | School of Seienee,Anshan University of Science and Technology,Anshan 114044,China |
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| Abstract: | The algebraic relations between the components of an augular momentum operator are of key importance in solving Schrodinger.In this paper we have exploited the dyadic product between vector products to deduce the coordinate-independent formula of scalar product and vector product between angular momentum operators.Then the formula for the scalar product of angular momentum operators is used to deduce the Schrodinger equation for one particle in spherical coordinate.In the final,we make a interest contrast among vector product,commutation relation and classical Poisson brackets,and find out their common properties that they all have the anti-commutative relationship and the Jacohi identity. |
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| Keywords: | angular momenturm operator dyadic Schrodinger equation |
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