Question

Question on QM

Answer 1

In Dirac's Principles of Quantum Mechanics he tries to derive the commutation relationship of the operator \(\frac{d}{dq}\) and the operator \(\hat{q}\) where q is the canonical coordinate. The problem is that he doesn't attach a hat to his operators and he writes \[\frac{d}{dq}q \psi \rangle =\frac{dq \psi}{dq}\rangle=q \frac{d \psi}{dq} \rangle + \psi \rangle\]In this equation he uses the product rule between an operator and a function which is false since it is not an usual multiplication and he further assumes that the derivative of the coordinate operator with respect to the coordinate is one, which is ill defined. Can somebody justify this?

Answer 2

All of this would be solved if somebody could explain to me why \[\hat{p} \psi \rangle =p \psi \rangle\]

Answer 3

I am sorry, it should be q instead of p