Is this reasoning correct or wrong?
In NRQM there is a state vector ## \ket \Psi## that has all the information about the system inside. Therefore, one cannot talk about position, velocity, acceleration, etc. The wave function is the state expressed in position basis, and its Fourier transform is the state expressed in momentum basis.
The expected value is the average value we get by repeating the experiment starting from the same initial conditions, and we can calculate them as follows: ##\braket{x}=\braket{\Psi|\hat x|\Psi}## and ##\braket{p}=\braket{\Psi|\hat p|\Psi}##, where ##\hat x## and ##\hat p## are operator associated with position and momentum.
If I want to get a quantity associated with acceleration, should I consider ##\frac{d\braket{p}}{dt}##?
By Ehrenfest's theorem this quantity is: ##\frac{d\braket{p}}{dt}=-\braket{\frac{\partial V}{\partial x}}##
Which under some conditions reproduces Newton's law $$F=ma$$ in classical mechanics.
Is this related to the concept of acceleration in NRQM or am I still getting it wrong?
What happens in QFT when a particle is accelerated?
I'm using a translator, sorry for mistakes.