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!

Basic QM - Trying to catch up in a class

  1. Aug 25, 2007 #1
    I haven't taken one of the recommended courses for a class I am in, so I'm playing a little catch-up here.

    Q: The wave function of an electron in a one-dimensional infinite square well of width a,x -> (0,a) at time t=0 is given by:

    [tex] \psi (x,0) \sqrt{\frac{2}{7}}\psi_1(x) + \sqrt{\frac{5}{7}}\psi_2(x) [/tex]

    where [tex] \psi_1(x) [/tex] and [tex] \psi_2(x) [/tex] are the ground and first excited stationary state of the system respectively, [tex] \psi_n(x)=\sqrt{\frac{2}{a}}\sin (n\pix/a), \,\,\, E_n = n^2\pi^2 \bar h^2/(2ma^2), \,], n=1,2,... [/tex]

    a) Write down the wavefunction at time t in terms of [tex] \psi_1(x) [/tex] and [tex] \psi_2(x) [/tex].

    b) You measure the energy of an electron at time t=0. Write down possible values of the energy and the probability of measuring each.

    c) Calculate the expectation value of hte enrgy in the state [tex] \psi(x,t) [/tex] above.

    ----
    I am lost here. I am stuck on (a) right now, and really do not know where to go. To me it looks like [tex] \psi_n(x) [/tex] is the wavefunction already solved from the schrodinger equation (with the boundary conditions 0 and a). So I need to express the total wavefunction in terms of two states psi_1, and psi_2. This to me seems like another condition that would come from a differential equation something with a time dependence. I am lost...

    Would someone nudge me in a proper direction?

    thanks,
     
  2. jcsd
  3. Aug 25, 2007 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    Hint for 1. [tex]\psi (t)=U(t)\psi=e^{\frac{1}{i\hbar}tH} \psi [/tex]

    Daniel.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Basic QM - Trying to catch up in a class
  1. Catching up (Replies: 12)

  2. Catching-up to problem (Replies: 1)

Loading...