First Order Form of Schrödinger Equation
首发时间:2015-05-27
Abstract:Based on the algebra of matrices we propose a general first order equation in three- dimension which can deduce the Schrödinger equation. The corresponding time-independent equation is also proposed for a general potential. Several constant potential problems including potential step problem and potential well problem are treated using this first-order equation, we obtain the non- relativistic quantum mechanical results of the Schrödinger equation. Moreover, for the finite potential well problem, the first-order relativistic correction of the energy is also obtained.
keywords: First-order form Schrödinger equation potential well potential step
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Schrödinger方程的一阶形式
摘要:Klein-Gordon方程关于时间和空间都是二阶的相对论方程,而Dirac方程对时间和空间都是一阶的相对论方程。Schrödinger方程是时间一阶而空间二阶的非相对论方程。本文提出了Schrödinger方程的三维一阶形式,类似于Dirac方程,它关于时间和空间都是一阶的,且可以导出Schrödinger方程。相应地也给出了任意势的定态方程。利用此方程,我们求解了两个常数势问题:阶梯势与有限势阱,都能给出Schrödinger方程的结果。而对于有限势阱的分离谱,还能给出能级的相对论一阶校正。因此我们的方程相当于一个半相对论方程。
关键词: 一阶形式 Schrödinger方程 有限势阱 阶梯势
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No.4644614623679143****
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