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.(adsbygoogle = window.adsbygoogle || []).push({});

If anyone can explain, thanks.

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# Question about Schrodinger equation, potential and energy

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