Dirac方程中的量子与经典对应

根据Heisenberg对应原理(HCP),在经典极限下厄密算符的量子矩阵元对应经典物理量的Fourier展开系数.将HCP应用到相对论领域的Dirac方程中,对于自由粒子和在匀磁场中的带电粒子,其量子算符的矩阵元在经典极限下对应着相对论物理方程的解.计算表明,在经典极限下量子期望值就是对应经典物理量的时间平均值.

Quantum and classical correspondence of Dirac equations

According to Heisenberg correspondence principle, quantum matrix element of a Hermitian operator reduces to the coefficient of Fourier expansion of the corresponding classical quantity in the classical limit. Applying HCP to Dirac equations in relativistic realm, for the relativistic free particle or the charged particle moving in a constant magnetic field, it is shown that quantum operators in Dirac theory reduces to the classical quantities in the classical limit and the classical limit of quantum expectation value is the time average of the classical quantity.