# Hamiltonian matrix problem

1. Dec 26, 2008

### Rajini

dear members,
My problem is...
suppose take the spin Hamiltonian Hham=D[Sz2 -S(S+1)/3 +(E/D)(Sy2-Sy2)] +Hi$$\vec{S}$$ (most often in EPR experiments, etc).
here external magnetic field Hamiltonian Hi = $$\beta$$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..
Rajini

2. Dec 27, 2008

### olgranpappy

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.

3. Dec 28, 2008

### Rajini

dear members,
My problem is...
suppose take the spin Hamiltonian Hham=D[Sz2 -S(S+1)/3 +(E/D)(Sx2-Sy2)] + $$\beta$$$$\vec{B}$$$$\tilde{g}$$$$\vec{S}$$ (most often in EPR experiments, etc).
here external magnetic field Hamiltonian Hi = $$\beta$$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..

4. Dec 28, 2008

### Rajini

Hi olgran, I corrected my error..