How to Label Spin Hamiltonian by Ms in EPR Experiments?

[Rajini]

dear members,
My problem is...
suppose take the spin Hamiltonian H_ham=D[S_z² -S(S+1)/3 +(E/D)(S_y²-S_y²)] +H_i\vec{S} (most often in EPR experiments, etc).
here external magnetic field Hamiltonian H_i = \betag_iB_i^ext and i =x, y and z. Also g_x=g_y=g_z=2 and the external magnetic field is parallel/along z-axis. M_s is the magnetic quantum number.
What i don't know.. Using S=5/2 and writing down in the |5/2,M_s> representation yields a matrix (from the above spin Hamiltonian)...I really don't know how to write it.(may be in other words how to label spin Hamiltonian by M_s )..But i have the solution...Can anyone help me?? I am really frustrated about this problem..
advance thanks for helping me..
Rajini

 

[olgranpappy]

dear members,
My problem is...
suppose take the spin Hamiltonian H_ham=D[S_z² -S(S+1)/3 +(E/D)(S_y²-S_y²)] +H_i\vec{S} (most often in EPR experiments, etc).
here external magnetic field Hamiltonian H_i = \betag_iB_i^ext and i =x, y and z. Also g_x=g_y=g_z=2 and the external magnetic field is parallel/along z-axis. M_s is the magnetic quantum number.
What i don't know.. Using S=5/2 and writing down in the |5/2,M_s> representation yields a matrix (from the above spin Hamiltonian)...I really don't know how to write it.(may be in other words how to label spin Hamiltonian by M_s )..But i have the solution...Can anyone help me?? I am really frustrated about this problem..
advance thanks for helping me..
Rajini

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 S_z looks like in the basis. Then write what S_+ (the raising operator) looks like and then what S_- looks like.

 

[Rajini]

dear members,
My problem is...
suppose take the spin Hamiltonian H_ham=D[S_z² -S(S+1)/3 +(E/D)(S_x²-S_y²)] + \beta\vec{B}\tilde{g}\vec{S} (most often in EPR experiments, etc).
here external magnetic field Hamiltonian H_i = \betag_iB_i^ext and i =x, y and z. Also g_x=g_y=g_z=2 and the external magnetic field is parallel/along z-axis. M_s is the magnetic quantum number.
What i don't know.. Using S=5/2 and writing down in the |5/2,M_s> representation yields a matrix (from the above spin Hamiltonian)...I really don't know how to write it.(may be in other words how to label spin Hamiltonian by M_s )..But i have the solution...Can anyone help me?? I am really frustrated about this problem..
advance thanks for helping me..

 

[Rajini]

Hi olgran, I corrected my error..
thanks for replying

 

[Rajini]

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