I would like to find the acceleration of an electron moving in a straight line from a point a to point b

There is uncertainty in observable quantities like acceleration. Plus, acceleration is not really a useful concept in QM. I think a better question to ask would be, "what is the probability for an electron to start at A and be detected at B in time t?" The answer is an amplitude called the "propagator," which is defined as: [math]K(x,x',t)= \langle x'|e^{-iHt/\hbar} |x \rangle[/math]. The amplitude squared gives you the probability.

Edited November 4, 201411 yr by elfmotat

It depends. There are plenty of situations where classical physics gives a reasonable answer involving single particles.

Alternatively you could examine a particle with larger mass, which, assuming it is stable, will make quantum effects less apparent.

I would like to find the acceleration of an electron moving in a straight line from a point a to point b

First of all, you should tell us "acceleration in what medium?"

 

When electron is emitted in vacuum, answer will be different than when electron is emitted in air.

Slow electron moving in air, can travel only very short distance.

Electron accelerated nearly to speed of light flying through air medium is causing ionization along its trace, and air molecules are slowing it down.

So suddenly it stops moving. And its trace is disappearing in that place.

 

This can be seen in Cloud Chamber.

 

Edited November 4, 201411 yr by Sensei