Eigenvalue Problem in Uniformly Acceleration Motion

[jshw]

Homework Statement

In Uniform Acceleration Motion, the force F is constant.
then potential V(x)=Fx, and Hamiltonian H=(p^2/2m)-Fx
The problem is to solve the eigenvalue problem Hpsi(x)=Epsi(x)

Homework Equations

F=constant
V(x)=Fx
H=(p^2/2m)-Fx

The Attempt at a Solution

I have tried to compare classical mechanics and quantum mechanincs.
but, my QM textbook don't mention about uniformly acceleration motion.
I had hard time to solve it during this weekend. but I get lost the direction to solve it.
I think that this problem is mathematically messy. please give me the direction to solve this problem.

 

[Pythagorean]

jshw,

I don't completely understand what you're asking.

I'm guessing Fx is the partial of F with respect to x, so is the potential (V(x)) Fx everywhere? in a one-dimensional setting? (i.e. is this a particle in a 1D box with constant potential across the bottom of the whole box?)

classically, I think 'uniformly accelerating' means that every part of an object is accelerating in same direction, at the same rate (as opposed to an object spinning through air, for instance) but I'm not sure what it means in the context of a single particle; perhaps it's as simple as constant acceleration...?

 

[logscale]

Your Hamiltonian certainly looks like having Airy function as a possible solution.