论文标题
伪质量参数化炼金术方程：分子schrödinger方程的概括
Pseudo-mass parameterized alchemical equation: a generalisation of the molecular Schrödinger equation
论文作者
论文摘要
我们引入了一个伪质量的参数化schrödinger样炼金术方程，该方程包含核电荷载，作为变量，处理核电，核电坐标和电子坐标。炼金术方程的本征函数是核电荷的波函数，就像传统波函数是坐标一样。给出了炼金术功能空间的数学定义，以保持“核电荷波函数”。还得出了炼金术动力学和炼金术相空间的几何相。对于氢样离子，炼金术方程可以简化为强反向平方电位方程，该方程是指量子异常，并保持非相关性量子力学中的保形不变性。也证明了在时间依赖性的夹紧核糖炼金术动力学中适用于非平稳状态的Hellmann-Feynman定理的扩展。
We introduce a pseudo-mass parameterized Schrödinger-like alchemical equation which contains nuclear charges as variables, treating nuclear charges, nuclear coordinates and electronic coordinates on the equal footing. The eigenfunctions of the alchemical equation are the wave functions of nuclear charges, just like conventional wave functions are of coordinates. A mathematical definition of alchemical function space is given to hold the ''nuclear charge wave function''. The geometric phase of alchemical dynamics and alchemical phase space are also derived. For hydrogen-like ion, the alchemical equation can be simplified into a strong repulsive inverse square potential equation, which refers to the quantum anomaly and keeps conformal invariance in non-relativistic quantum mechanics. An extension of the Hellmann-Feynman theorem, which applies to the non-stationary state in time-dependent clamped-nuclear-charge alchemical dynamics, is also proved.
