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My confusion maybe incredibly dumb, so I want to apologise beforehand (if the question is too dumb, please just let me know the answer in a comment and I'll delete it after to avoid clogging up S.E. with rubbish). I decided to look into examples applications of the Schrodinger equation. In particular, the finite potential barrier example.

What I'm confused about is this: if ${E < V_0}$, then the wave function is real and non-zero within the potential barrier region, meaning that there is a non-zero probability within that region. Wouldn't this mean the kinetic energy has to be negative in order to conserve energy if the particle was found to be in that region upon measurement?

Qmechanic
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