Hi everyone, This question is from my problem set this week in my Phys 371 class. Any help, hints or ideas would be very much appreciated!(adsbygoogle = window.adsbygoogle || []).push({});

"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.

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Ground state energy of hydrogen atom

Loading...

Similar Threads - Ground state energy | Date |
---|---|

I How can an atom change from ground to excited state? | Mar 12, 2017 |

Effect of spins on hydrogen atom ground state energy | Jan 27, 2016 |

Ground state energies and potential | Jan 20, 2016 |

Ground-state energy of harmonic oscillator(operator method) | Dec 12, 2015 |

**Physics Forums - The Fusion of Science and Community**