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

Energy expectation values of harmonic oscillator

  1. Mar 30, 2010 #1
    I'm looking at a question....

    The last part is this: find the expectation values of energy at t=0

    The function that describes the particle of mass m is


    where I've found A to be 1/sqrt2. The energy eigenstates are [tex]\varphi[/tex]_n with eigenvalue E_n=(n + 1/2)hw

    I tried the usual expectation value way but I run into a horrible sum which seems to diverge I think. How shouldf I go about this??

    Cheers guys!!
  2. jcsd
  3. Mar 30, 2010 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    The sum shouldn't diverge because of the [itex](1/\sqrt{2})^n[/itex] factor. You can split it into two series. One will be geometric, so it's easy to sum. The other one may require slightly more work to sum, but it's pretty straightforward. Hint: Consider the series for [1/(1-x)]'.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook