1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Effect of the Harmonic Oscilator Raising and Lowering Operators on Time Dependance

  1. Aug 2, 2009 #1
    I am not really asking how to solve the problem but just for explanation of what I know to be true from the problems solution. Basically the original problem statement is this:

    A particle in a harmonic oscillator potential starts out in the state
    |psi(x,0)>=1/5 * [3|0> + 4|1>] and it asks to find the expectation value of position <x>.

    Now the way I approached the problem was to first find |psi(x,t)> by simply "tacking on" the time dependent exponential terms and then expressing x through the ladder operators a+ and a-.

    What I am wondering is when I, for example, apply the raising operator a+ to the state |0>*exp(-i*E0*t/h) does the function become |1>*exp(-i*E0*t/h) rather than |1>*exp(-i*E1*t/h) (i.e. why does the energy term in the time dependent part not change?)

    Thanks!
     
  2. jcsd
  3. Aug 2, 2009 #2

    kuruman

    User Avatar
    Homework Helper
    Gold Member

    Re: Effect of the Harmonic Oscilator Raising and Lowering Operators on Time Dependanc

    The energy terms E1 and E0 are constants, namely multiples of [tex]\hbar[/tex][tex]\omega[/tex]. Put in these values, if you wish, before you operate with the ladder operators and see what happens.
     
  4. Aug 2, 2009 #3
    Re: Effect of the Harmonic Oscilator Raising and Lowering Operators on Time Dependanc

    Ah o.k. I see now, thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Effect of the Harmonic Oscilator Raising and Lowering Operators on Time Dependance
Loading...