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 Physics Help

  1. Feb 5, 2010 #1
    Quantum Physics Help!!

    1. The problem statement, all variables and given/known data
    The spring constant for a particle in the ground state of a simple harmonic oscillator changes by a factor a^4 instantaneously, what is the probability that the particle is observed in the ground state of the new potential immediately following the change

    can anyone give me a step in the right direction please, i think i have to use perturbation theory, but havent really been taught how to

    2. Relevant equations
    v(x)=(a^4)(kx^2)/2 is the new potential



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 5, 2010 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Re: Quantum Physics Help!!

    There's no need for perturbation theory here. Just ask yourself two questions:

    (1)What is the ground state of the harmonic oscillator both before and after the change in spring constant?

    (2)If I'm told that a particle is in the state [itex]|\psi_1\rangle[/itex] and I want to find the probability that it is measured in the state [itex]|\psi_2\rangle[/itex], what equation would I use?

    The answer to number (1) is derived in most introductory QM texts, and the answer to number (2) is often taken to be one of the postulates of QM.
     
  4. Feb 6, 2010 #3
    Re: Quantum Physics Help!!

    so the ground state before is (1/a(sqrt Pi))^1/2 exp[-x^2/2a^2] where a=(h_bar/mw)^1/2
    and w=(k/m)^1/2 so the ground state after is the same but w=(a^4k/m)^1/2 ?

    so then calculate c=integral (psi*Psi(x,0))dx
    and then c^2 is the probability?

    does this seem about right?
     
  5. Feb 6, 2010 #4

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    Re: Quantum Physics Help!!

    Seems about right to me:smile:
     
  6. Feb 6, 2010 #5
    Re: Quantum Physics Help!!

    sorry to keep asking questions, i think im being a bit stupid, just to clarify something, in my above post would Psi(x,0) be my initial wavefunction, the one where the potential has not changed, and psi* would be the wavefunction when the potential has changed?
    thanks
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook