Constructs spin Hamiltonian operators.
[F,Gx,Gy,Gz] = sham(Sys) [F,G] = sham(Sys,B) H = sham(Sys,B)
This function returns the
spin Hamiltonian or its components. Sys
is the structure defining the spin system, the optional B
is the
3-element external magnetic field vector (in mT) in the molecular
frame of the spin system.
If no magnetic field is given, sham
returns the four Hamiltonian
components
F
, Gx
, Gy
and Gz
.
F
is the Hamiltonian
containing all field-independent interactions, and the other three
matrices are the components of the Zeeman interaction Hamiltonian for the
three principal directions of the molecular frame of the spin system (see
zeeman).
If a magnetic field B
is given, sham
returns either the overall
Hamiltonian H
or its two components F
(field-independent
interactions) and G
(Zeeman interactions along the direction of B
).
F
and H
are in MHz, the components
G
, Gx
, Gy
and
Gz
are in MHz/mT.
The general form of the spin Hamiltonian and the terms contained in it are explained in the section about the spin system structure.
The Hamiltonian of a simple S=I=1/2 system is
g = [2 2 2]; A = [1 1 2]*100; B = [0 0 340]; Sy = struct('S',.5,'g',g,'Nucs','1H','A',A); H = sham(Sy,B)
H = 1.0e+03 * 4.8015 0 0 0 0 4.7160 0.0500 0 0 0.0500 -4.8160 0 0 0 0 -4.7015
To get its eigenvalues in GHz and their associated eigenvectors, use
[V,E] = eig(H); E = diag(E).'/1e3, V
E = -4.8162 -4.7015 4.7162 4.8015 V = 0 0 0 1.0000 -0.0052 0 -1.0000 0 1.0000 0 -0.0052 0 0 1.0000 0 0
eeint, hfine, internal, nquad, zeeman, zfield