Expressions for the first-order polarization charge density ρ⁽¹⁾ and current density J⁽¹⁾ induced in a molecule by a monochromatic plane wave, obtained by time-dependent quantum mechanical perturbation theory, have been investigated to assess their gauge invariance and independence of the coordinate system in passive and active translations. The conditions arrived at show that, within the (long wavelengths) dipole approximation, only the electric contributions to these densities are needed to rationalize the phenomenology. To the next higher quadrupole approximation, assuming that the magnetic field and the electric field gradient are uniform over the molecular dimensions, corresponding contributions to ρ⁽¹⁾ and J⁽¹⁾ are considered. It has been found that total densities are independent of the origin, whereas the contributions from electric and magnetic fields are not separately invariant. A magnetic contribution to J⁽¹⁾, which is by itself origin independent, can be defined by means of an approach based on continuous translation of the origin of the coordinate system.

中文翻译：

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光场引起的电子电荷密度和电流密度的量规不变性和原点无关性

研究了由时变量子力学微扰理论获得的单色平面波在分子中诱导的一阶极化电荷密度ρ ^（1）和电流密度J^（1）的表达式，以评估其尺度不变性和独立性被动翻译和主动翻译中的坐标系。得出的条件表明，在（长波长）偶极近似内，仅需要对这些密度的电贡献即可使现象学合理化。对于下一个更高的四极近似，假设磁场和电场梯度在分子尺度上是均匀的，则对ρ ^（1）和考虑J^（1）。已经发现总密度与原点无关，而电场和磁场的贡献并不是分别不变的。可以通过基于坐标系原点连续平移的方法来定义对J^（1）的磁贡献，其本身与原点无关。