Calculates energy levels of a spin system in an external field.

out = levels(SpinSystem,phi,theta,B)

This function determines energy levels of the spin system specified in the structure SpinSystem by diagonalising its Hamiltonian. The external field is specified in the other three function arguments.

theta is the angle between the z axis of the molecular frame and the magnetic field vector, phi is the angle between x axis and the projection of the magnetic field vector on the xy plane of the molecular frame. B gives the magnitude of the magnetic field in mT.

out is a vector of the energies of the eigenstates of SpinSystem, in ascending order. The energies are in MHz.

phi, theta and B can be vectors, in which case energy levels for all possible combinations of their values are calculated. Depending on the dimensions of the three parameters, the output out can be an up to 4-dimensional array. The energies are always along the last dimension.

A scalar theta together with vectors phi and B would yield a 3D array out. A set of energies for a single magnetic field orientation is then in out(k,l,:) with k and l indexing phi and B, respectively.

The three lines

Sy = struct('S',5/2,'g',[2 2 2],'D',[-250 -1750 2000]);
B = 0:500; E = levels(Sy,0,0,B);
plot(B,E)

produce a plot of the quite complicated dependence of the energy levels of a spin-5/2 system on the external magnetic field magnitude. A number of level anticrossings are present.

levelsplot, eigfields, resfields, sham