Matrix representations of spin operators.

S = sop(SpinSystem,Comps)
[S1,S2,...] = sop(SpinSystem,Comps1,Comps2,...)
... = sop(...,'sparse');

sop returns the matrix representation of spin operators. The representation is in the product basis |m_I1,m_I2,m_I3,..>. with the basis functions in descending m_I order, left to right. E.g. for a system with one electron-1/2 and one nucleus with spin 1 the states are in the following order: |1/2,+1>, |1/2,0>, |1/2,-1>, |-1/2,+1>, |-1/2,0>, |-1/2,-1>.

SpinSystem is a vector containing the spin quantum numbers or, alternatively, a spin system structure. Comps is a string specifying one operator component for each spin in SpinSystem. Elements of Comps can be 'e' (identity), 'x' (I_x), 'y' (I_y), 'z' (I_z), '+' (I₊) or '-' (I_-). The order in Comps corresponds to the order in SpinSystem. E.g. for a 3-spin system Comps = 'ye-' yields .

More than one component string can be specified, in which case sop computes all operators at once. Of course, there must be a corresponding number of output arguments.

If 'sparse' is given as last argument, spin operator matrices are returned in sparse instead of full form.

Splus = sop(1/2,'+')

Splus =
     0     1
     0     0

SzIx = sop([1/2 1/2],'zx')

SzIx =
         0    0.2500         0         0
    0.2500         0         0         0
         0         0         0   -0.2500
         0         0   -0.2500         0

To compute multiple operators with one call, use for example

[Sx,Sy,Sz] = sop(1,'x','y','z');

Sx =
         0    0.7071         0
    0.7071         0    0.7071
         0    0.7071         0
Sy =
        0                  0 - 0.7071i        0
        0 + 0.7071i        0                  0 - 0.7071i
        0                  0 + 0.7071i        0
Sz =
     1     0     0
     0     0     0
     0     0    -1

Instead of the spin quantum numbers, a spin system structure can be provided.

System.S = 1;
System.g = 2;
System.D = [1000 0];
sop(System,'-')

ans =
         0         0         0
    1.4142         0         0
         0    1.4142         0

spin operators, spin system, spinvec, stev