- #1

MxwllsPersuasns

- 101

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## Homework Statement

I'm currently working on a homework set for my intermediate QM class and for some reason I keep drawing a blank as to what to do on the first problem. I'm given three potentials, V(x), the first is of the form {A+Bexp(-Cx^2)}, the others I'll leave out. I'm asked to draw the potential (easy enough) and also then to state the range (if any) of the bound-state energies (discrete eigenvalues of the Hamiltonian) and also state the range (if any) of the non-bound state energies (continuous range of eigenvalues of the Hamiltonian).

## Homework Equations

## The Attempt at a Solution

I think I understand that a bound state is one which (simply put) decays to zero at or before infinity, in other words the energy of the particle in the 1D well is less than 0 but greater than the negative potential energy.

So for my example V(x) above I notice that the max for the potential is achieved at (0, A+B) and that my potential decays to A quickly then remains there until +(inf) and as x trends towards -(inf) V(x) trends towards +(inf). So then would the whole of the plane be a bound state for this potential? Also how would I determine these discrete eigenvalues (bound state energies) and continuous eigenvalues (non bound state energies)? Any help is GREATLY appreciated. Thanks for taking the time to read through my post :)