Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Quantum Mechanics and the Hydrogen Atom

  1. Nov 3, 2011 #1
    Calculate the expectation value of the potential energy for an electron in a 1s orbital for a hydrogen atom

    Ive determined the potential energy operator to be V=-e2/4∏ε0r
    and a wave function of

    ψ= (1/4∏)1/2

    therefore i get
    <V> = ∫∫∫ψ*Vψr2sin∅drd∅dphi
    integrals from 0 to r, 0 to pi, 0 to 2pi

    not sure where to go from here.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Nov 3, 2011 #2
    Nevermind, i got it.

    but if anyone is interested ill explain.

    For a 1s orbital of a hydrogen the wavefunction is ψ=root(1/∏ao3 e-r/ao)

    this gives
    integrals are zero to 2pi, zero to pi, and zero to infinity.

    then factor out any terms that are not a function of r,θ, or∅.
    This gives several terms outside of the integral: ∫∫∫e-2r/aorsinθdrdθd∅

    then you can separate the integrals and evaluate. they were pretty easy to do.

    the final answer was <v> = -e2/4∏εoao
  4. Nov 4, 2011 #3


    User Avatar
    Science Advisor
    Homework Helper

    You can use the virial theorem. The expectation value you're looking for is then half the ground state energy.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook