qspec.hyper_zeeman_12  (  j ,  m ,  a_hyper = 0.0 ,  g_i = 0.0 ,  g_j = 0.0 ,  b_field = 0.0 ,  g_n_as_gyro = False ,  as_freq = True  )[source]

The two eigenvalues of the hyperfine structure + Zeeman effect hamailtonian for a nuclear spin of $I=1/2$ and the magnetic quantum number m, calculated analytically using the Breit-Rabi equation.

Parameters:

jquant_like

The electronic total angular momentum quantum number $J$.

mquant_like

The magnetic quantum number $m_F$.

a_hyperarray_like

The magnetic dipole hyperfine constant $A = \mu_I \mathcal{B}_J / (IJ)$ (MHz if as_freq else eV).

g_iarray_like

The nuclear g-factor $g_I$ or the gyromagnetic ratio $\gamma_I$ if g_n_as_gyro == True.

g_jarray_like

The electronic g-factor $g_J$.

b_fieldarray_like

The B-field $\mathcal{B}$ (T).

g_n_as_gyrobool

Whether g_i is the nuclear g-factor or the gyromagnetic ratio $\gamma_I$ (MHz).

as_freqbool

The shift can be returned in energy (False, eV) or frequency units (True, MHz). The default is True

Returns:

(x0, x1)(ndarray, ndarray)

The two solutions of the Breit-Rabi equation, where x0 and x1 correspond to $F = J \mp 1/2$, respectively.