Acceleration. Infinite potential well.

[LagrangeEuler]

Why we don't have acceleration in quantum mechanics. For example why particle in infinite potential well can not accelerate. For example dimension of well is $L$ and $L=\frac{at^2}{2}$, where $a$ is acceleration.

 

[jtbell]

For example dimension of well is $L$ and $L=\frac{at^2}{2}$, where $a$ is acceleration.

What's your reasoning here? In the usual infinite square well, the potential is constant (zero) inside the well. Classically, the force on the particle would be zero everywhere except at the walls, like a molecule in an ideal gas. The particle's acceleration would also be zero at all times except when it's colliding with one of the walls.

More important, in order to talk about the acceleration of a particle, it has to have a trajectory: a well-defined position as a function of t. In QM we don't have that, except in the Bohmian interpretation where the trajectories are highly non-classical anyway.

 

[ChrisVer]

Additionally, it would be weird to talk about acceleration for any system which has discrete energy states... acceleration would mean that the particle would gain/lose energy in some continuous amounts, and that would need it to change its energy respectively...
In the same way someone would say that the electron accelerating inside the atom, would have to radiate its energy and "fall" into the nucleus...

Of course I believe fundamentally the reason is what jtbell stated in #2

 

[LagrangeEuler]

Well I define in potential well that $\langle p \rangle=0$. Could I interprete this like particle goes from left to right as much as it goes from right to left in the well. So I can say that impulse in one direction is $p$, and in the other is $-p$ so $\langle p \rangle=0$. Why the particle does not loose some energy in contact with the walls.

 

[ChrisVer]

because the walls are very strong...
If you had a finite well potential, there would be penetration/transition...

Yes you can, interpret it like that. But that's only because the mean values behave like classical quantities...