arc.alkali_atom_functions.AlkaliAtom.radialWavefunction#

AlkaliAtom.radialWavefunction(l, s, j, stateEnergy, innerLimit, outerLimit, step)[source]#

Radial part of electron wavefunction

Calculates radial function with Numerov (from outside towards the core). Note that wavefunction might not be calculated all the way to the requested innerLimit if the divergence occurs before. In that case third returned argument gives nonzero value, corresponding to the first index in the array for which wavefunction was calculated. For quick example see Rydberg wavefunction calculation snippet.

Parameters

  • l (int) – orbital angular momentum

  • s (float) – spin angular momentum

  • j (float) – total angular momentum

  • stateEnergy (float) – state energy, relative to ionization threshold, should be given in atomic units (Hatree)

  • innerLimit (float) – inner limit at which wavefunction is requested

  • outerLimit (float) – outer limit at which wavefunction is requested

  • step (flaot) – radial step for integration mesh (a.u.)

Returns

\(r\)

\(R(r)\cdot r\)

Return type

List[float], List[flaot], int

Note

Radial wavefunction is not scaled to unity! This normalization condition means that we are using spherical harmonics which are normalized such that \(\int \mathrm{d}\theta~\mathrm{d}\psi~Y(l,m_l)^* \times Y(l',m_{l'}) = \delta (l,l') ~\delta (m_l, m_{l'})\).

Note

Alternative calculation methods can be added here (potenatial package expansion).