ham

Constructs spin Hamiltonian matrix

Syntax

[H0,mux,muy,muz] = ham(Sys)
[H0,mux,muy,muz] = ham(Sys,'sparse')
H = ham(Sys,B)
H = ham(Sys,B,'sparse')

Description

This function returns the matrix representation of 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) defined in the molecular frame of the spin system.

If no magnetic field is given, ham returns the four Hamiltonian components H0, mux, muy and muz. H0 is the Hamiltonian containing all field-independent interactions, and the other three matrices are the components of the magnetic dipole moment operator along the three principal directions of the molecular frame of the spin system (see ham_ez, ham_nz and ham_oz).

If a magnetic field B is given, ham returns the overall Hamiltonian H.

To construct H from H0, mux, muy, muz and B, use H = H0 - B(1)*mux - B(2)*muy - B(3)*muz.

H and H0 are in units of MHz, and mux, muy and muz are in units of MHz/mT (= GHz/T).

The general form of the spin Hamiltonian and the terms contained in it are explained in the section about the spin system structure.

If 'sparse' is given as last input argument, the Hamiltonian matrix is returned in sparse format instead of full format.

Examples

The Hamiltonian of a simple S=I=1/2 system is

Sys.g = 2;
Sys.A = [1 1 2]*180;
Sys.Nucs = '1H';
B = [0 0 340];
H = ham(Sys,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;
E, 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