Scalar and vector potentials in electromagnetism. The scalar potential is potential energy per unit charge. For potential energy, use the potential-energy tag.

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Eigenvalues of the radial Schrödinger equation on a finite integration interval

There are numerous ways to estimate the eigenvalues of a radial Schrödinger equation, see http://arxiv.org/abs/math-ph/0703040 as an example. Anyhow, the formulas only cover the Schrödinger equations ...
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General question about the potential barrier problem: Why does $\exp( kx)$ diverge when $x>0$ in the case when $E < V(x)$?

For the two images below, the first potential barrier has particles approaching it where $E > V_o$ & the second has a particle that has $E < V_o$, where $E$ is the energy of the particles ...