薛定谔方程的规范变量对称性
Gauge Variant Symmetries for the Schrödinger Equation
摘要：
最后一个乘子的雅可比提供了一个路线，确定家庭的拉格朗日为一个给定的系统。我们表明，一个家庭的成员是等价的，因为他们不同的总时间导数。我们推导出一个带有常数乘子的单自由度系统的薛定谔方程。下面我们考虑简谐振子的特殊例子。对于含有任意函数的简谐振子的一般方程，我们证明了所有的薛定谔方程在同一代数上具有相同数目的李点对称.从对称性出发，我们构造了薛定谔方程的解，发现它们的差别仅在于由规范决定的相位。
英文摘要：
The last multiplier of Jacobi provides a route for the determination of families of Lagrangians for a given system. We show that the members of a family are equivalent in that they differ by a total time derivative. We derive the Schrödinger equation for a one-degree-of-freedom system with a constant multiplier. In the sequel we consider the particular example of the simple harmonic oscillator. In the case of the general equation for the simple harmonic oscillator which contains an arbitrary function we show that all Schrödinger equations possess the same number of Lie point symmetries with the same algebra. From the symmetries we construct the solutions of the Schrödinger equation and find that they differ only by a phase determined by the gauge.
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