- #1

- 64

- 0

## Main Question or Discussion Point

I have a question that's driving me insane and I'm sure there's a simple answer that I'm missing for some reason, but I'm not getting my a-ha moment.

Consider 2 cases from intro QM:

Infinite square well

Potential barrier with E > V

For the infinite square well, the Schrodinger eqn gives

d2ψ/dx2 + k

Since k

For the potential barrier with E > V0, the Schrodinger eqn gives (with the potential jumping from 0 to V

d

prior to the potential step (i.e. for x < 0) and

d

after the potential step (for x > 0)

My problem is this: As far as I can tell, both k

Am I making a sign error here or just forgetting something from differential equations? What is different about these equations that one of them gives oscillating, and the other non-oscillating, solutions?

Thanks for any help!

Consider 2 cases from intro QM:

Infinite square well

Potential barrier with E > V

_{0}For the infinite square well, the Schrodinger eqn gives

d2ψ/dx2 + k

^{2}ψ = 0Since k

^{2}> 0, this gives oscillating solutions (some combination of sines and cosines). Correct?For the potential barrier with E > V0, the Schrodinger eqn gives (with the potential jumping from 0 to V

_{0}at x = 0)d

^{2}ψ/dx^{2}+ k^{2}_{I}E = 0 (where k_{I}= √2mE/(hbar^{2})prior to the potential step (i.e. for x < 0) and

d

^{2}ψ/dx^{2}+ k^{2}_{II}E = 0 (where k_{II}= √2m(E-V0)/(hbar^{2})after the potential step (for x > 0)

My problem is this: As far as I can tell, both k

_{I}and k_{II}are positive numbers (since E > V_{0}> 0). Why, then, do they give non-oscillating solutions? Whereas, for the infinite square well, a positive k gave oscillating solutions?Am I making a sign error here or just forgetting something from differential equations? What is different about these equations that one of them gives oscillating, and the other non-oscillating, solutions?

Thanks for any help!