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Hamiltonian matrix problem

  1. Dec 26, 2008 #1
    dear members,
    My problem is...
    suppose take the spin Hamiltonian Hham=D[Sz2 -S(S+1)/3 +(E/D)(Sy2-Sy2)] +Hi[tex]\vec{S}[/tex] (most often in EPR experiments, etc).
    here external magnetic field Hamiltonian Hi = [tex]\beta[/tex]giBiext and i =x, y and z. Also gx=gy=gz=2 and the external magnetic field is parallel/along z-axis. Ms is the magnetic quantum number.
    What i dont know.. Using S=5/2 and writing down in the |5/2,Ms> representation yields a matrix (from the above spin Hamiltonian)...I really dont know how to write it.(may be in other words how to label spin Hamiltonian by Ms )..But i have the solution...Can anyone help me?? I am really frustrated about this problem..
    advance thanks for helping me..
    Rajini
     
  2. jcsd
  3. Dec 27, 2008 #2

    olgranpappy

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    Homework Helper

    First, it looks like you have some typos in your expression for H_{ham}. E.g., S_y^2 - S_y^2 is just zero. Also, the last term appears to be a vector.

    But, anyways, I think you should start by writing down what [itex]S_z[/itex] looks like in the basis. Then write what [itex]S_+[/itex] (the raising operator) looks like and then what [itex]S_-[/itex] looks like.
     
  4. Dec 28, 2008 #3
    dear members,
    My problem is...
    suppose take the spin Hamiltonian Hham=D[Sz2 -S(S+1)/3 +(E/D)(Sx2-Sy2)] + [tex]\beta[/tex][tex]\vec{B}[/tex][tex]\tilde{g}[/tex][tex]\vec{S}[/tex] (most often in EPR experiments, etc).
    here external magnetic field Hamiltonian Hi = [tex]\beta[/tex]giBiext and i =x, y and z. Also gx=gy=gz=2 and the external magnetic field is parallel/along z-axis. Ms is the magnetic quantum number.
    What i dont know.. Using S=5/2 and writing down in the |5/2,Ms> representation yields a matrix (from the above spin Hamiltonian)...I really dont know how to write it.(may be in other words how to label spin Hamiltonian by Ms )..But i have the solution...Can anyone help me?? I am really frustrated about this problem..
    advance thanks for helping me..
     
  5. Dec 28, 2008 #4
    Hi olgran, I corrected my error..
    thanks for replying
     
  6. Dec 28, 2008 #5
    Hi Olgran, I got a hint from your reply..(S- and S+)...based on ur hint...i am on the way:- solving my problem..hopefully i can solve it..after working on big 6x6 matrices..
    thanks
    rajini
     
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