On the Derivation of the Time-Dependent Equation of Schro dinger

for some quantum system S it is usually pointed out that time is a parameter, not enjoying the status of a quantum operator. However, it is almost never pointed out that the time occurring in HS(t) always is a classical time arising from the classical time development (according to Newton or Maxwell equations) of external fields or material particles interacting with the quantum system. In this sense the TDSE is, from the outset, a mixed quantum-classical equation. Having postulated Eq. (1), the authors of standard quantum mechanics text books then discuss the special case of