量子化学课程中物理量量子化的定义及应用

Definition of Quantization of Physical Quantities and Its Application in Quantum Chemistry Course

基于时间、空间、动量、能量存在最小基元的假设,证明了定义域区间内任意态函数均可写成正交归一动量本征态叠加的结论。不同于Dirac位置本征态的定义,基于量子化假设重新定义了位置本征态,讨论了位置本征态和位置叠加态的归一性。基于动量和坐标的定义域依据傅立叶变换给出了动量空间和坐标空间的正交基函数系。据此得出,在某些方面,重新定义的位置本征态优于传统位置本征态。

Under the condition that there is a minimum unit of time, length, momentum and energy, the state function can be constructed by orthonormal momentum eigenstates.The traditional Dirac position eigenstate in quantum mechanics was redefined according to the assumption that there was a minimum unit of length, and the normalization property of position eigenstate and superposition state was discussed.The orthogonal eigenfunctions were presented based on the quantization hyposesis of momentum and length.In addition, it was concluded that, in some aspects, the redefined position eigenstate had some advantages compared with traditional position eigenstate.