qspec.hyper_zeeman_num  (  i ,  j ,  hyper_const = 0.0 ,  gi = 0.0 ,  gj = 0.0 ,  b_field = 0.0 ,  g_n_as_gyro = False ,  as_freq = True  )[source]

The shifted energies/frequencies of the hyperfine structure states generated by the quantum numbers $I$ and $J$. This function numerically calculates the full diagonalization of the Hyperfine-structure + Zeeman-effect Hamiltonian $$ H = \sum\limits_{k=1}^{3} \left[\mathbf{T}_I^{(k)}\otimes\mathbf{T}_J^{(k)}\right]^{(0)} - \vec{\mu}_F\cdot\vec{\mathcal{B}}. $$

Parameters:

iquant_like

The nuclear spin quantum number $I$.

jquant_like

The electronic total angular momentum quantum number $J$.

hyper_constarray_like

The hyperfine structure constants $A = \mu_I \mathcal{B}_J / (IJ)$, $B = eQ_I (\partial^2 V_J / \partial z^2)$ and $C = \Omega_I T_J^{(3)}$ of the magnetic dipole, electric quadrupole and magnetic octupole order, respectively. If a scalar is given, only the $A$ constant is used (MHz if as_freq else eV).

giarray_like

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

gjarray_like

The electronic g-factor $g_J$.

b_fieldarray_like

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

g_n_as_gyrobool

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

as_freqbool

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

Returns:

(e_eig, m_list, f_list, mi_mj_list)(list[ndarray], list[quant], list[list[quant]], list[list[tuple[quant, quant]]])

The eigenvalues of the Hamiltonian $H$ sorted according to lists of $m_F$, $F$ and $(m_I, m_J)$, which are returned as the second to forth arguments.