- #1
Nylex
- 552
- 2
Ok, I know that the 1D time-independent Schrodinger equation is [tex]-\frac {\hbar^2} {2m} \frac {d^2 \psi(x)} {dx^2} + V(x) \psi(x) = E \psi(x)[/tex]. Why is it that you can mix potentials and energies in the same equation? For example, if you're saying that V(x) has a constant value, say, [tex]V(x) = V_{0}[/tex] and you're talking about a potential step, then you get something like [tex]k = \frac {\sqrt{2m(V_{0} - E)}} {\hbar}[/tex] for the wavenumber if the total energy is less than the step height. How can you subtract two different quantities? It doesn't make sense to me :(. I guess I didn't think about this much before now, when we've been set a problem where we're given values for E (in eV) and V (in V). Does the potential need to be converted to an energy first? It seems other people have been getting confused by this as well, so it isn't just me.
If anyone can explain, thanks.
If anyone can explain, thanks.