标题： 非相对论和相对论量子力学的能量算符再审视 显示英文标题

标题： Energy operator for non-relativistic and relativistic quantum mechanics revisited

摘要： 哈密顿算符是规范依赖的。 为克服这一困难，我们重新考察了规范变换对薛定谔方程和狄拉克方程的影响。 我们表明，算符$H-i\hbar\frac{\partial}{\partial t}$的规范不变性提供了一种从第一原理出发找到能量算符的方法。 特别是，当系统具有定态时，可以在非相对论和相对论量子力学中无歧义地识别能量算符。 最后，我们检查了其他方法，发现当电磁场与时间无关时，此处得到的能量算符与陈等人最近提出的算符相同。 [1] 显示英文摘要

摘要： Hamiltonian operators are gauge dependent. For overcome this difficulty we reexamined the effect of a gauge transformation on Schr\"odinger and Dirac equations. We show that the gauge invariance of the operator $H-i\hbar\frac{\partial}{\partial t}$ provides a way to find the energy operator from first principles. In particular, when the system has stationary states the energy operator can be identified without ambiguities for non-relativistic and relativistic quantum mechanics. Finally, we examine other approaches finding that in the case in which the electromagnetic field is time independent, the energy operator obtained here is the same as one recently proposed by Chen et al. [1].