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"Use the Heisenberg Uncertainty Principle to estimate the ground state energy in the hydrogen atom. Since the wave function that solves this problem is not a Gaussian, it will work best if you use [tex]\sigma_{r}[/tex][tex]\sigma_{p}[/tex]=[tex]\hbar[/tex]."

Where [tex]\sigma_{r}[/tex] is the standard deviation of the radius centered at the nucleus and [tex]\sigma_{p}[/tex] is the standard deviation of the momentum of the electron.

What I tried so far is to get the momentum in terms of the kinetic energy p=sqrt(2m(E-V)) [where V is the potential energy and E-V is the kinetic] and then put V in terms of r, since it would just be the coulomb potential energy........the trouble is that the algebra is devastatingly complicated and rather tedious when I try to solve for E--so it seems like there should be an easier way. Also, seems dubious to have E in terms of r without knowing what r is.