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!

Is the eigenstates of p right?

  1. Aug 18, 2008 #1
    Quantum Arnold’s cat is a special system.
    The Hamiltonian is H=p2+Kq2[tex]\delta[/tex]1(t)/2, where p[tex]\in[/tex](0,1],q[tex]\in[/tex](0,1].
    The system is in an N-dimensional Hilbert space, where N=1/h.
    Thus we can define : The eigenstates of [tex]\widehat{q}[/tex] are |j>, j=1,….,N, and the eigenstates of [tex]\widehat{p}[/tex] are |L>, L=1,…,N.
    So [tex]\hat{q}[/tex]|j>=[tex]\frac{j}{n}[/tex]|j>, [tex]\hat{p}[/tex]|L>=[tex]\frac{L}{N}[/tex] |L>.

    Now let’s obtain the eigenstates of [tex]\hat{p}[/tex].
    Because [tex]\hat{p}[/tex]|L>=[tex]\frac{L}{N}[/tex] |L>, -ih[tex]\frac{d\psi(q)}{dq}[/tex]=L/N[tex]\psi(q)[/tex].
    Therefor the eigenstates of [tex]\hat{p}[/tex] is [tex]\psi(q)[/tex]=exp(i2[tex]\pi[/tex]Lq).

    Is it right?
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted



Similar Discussions: Is the eigenstates of p right?
  1. Energy eigenstates (Replies: 4)

  2. Proving an eigenstate (Replies: 6)

  3. Common eigenstates (Replies: 7)

  4. Position eigenstates (Replies: 89)

Loading...