Harmonics#
Utilities for harmonics.
HarmonicsPG#
HarmonicsPG manages a set of point-group harmonics (real).
- class HarmonicsPG(pg_tag)[source]#
Bases:
dict
initialize the class.
- Parameters:
pg_tag (TagGroup or str) -- tag of point group.
- group(rank, axial=False)[source]#
group for given rank and i_type.
- Parameters:
rank (int) -- rank.
axial (bool, optional) -- axial ?
- Returns:
irreps. with given rank and i_type, (irrep., multiplicity).
- Return type:
[(str,int)]
- select(**kwargs) list[Harmonics] [source]#
select harmonics with given keywords.
- Parameters:
kwargs (dict) -- select conditions for harmonics, acceptable keywords are common to TagMultipole.
- Returns:
selected harmonics.
- Return type:
- tag#
point-group tag.
Harmonics#
Harmonics manages point-group harmonics.
- class Harmonics(m_tag, def_ex, ex, u)[source]#
Bases:
object
initialize the class.
- Parameters:
m_tag (TagMultipole or str) -- multipole tag.
def_ex (str) -- definition of harmonics in terms of tesseral harmonics.
ex (str) -- cartesian expression.
u (str) -- unitary matrix from Olm in descending order in m, [l,l-1,...,-l].
- classmethod create_equivalent_operator(poly, j)[source]#
equivalent operator in descending order in Jz.
- Parameters:
poly (str) -- (x,y,z) polynomial.
j (str) -- magnitude of angular momentum, J (0, 1/2, 1, ...).
- Returns:
equivalent-operator matrix.
- Return type:
NSArray
- definition()[source]#
definition of harmonics in terms of linear combination of Clm and Slm.
- Returns:
definition of harmonics.
- Return type:
NSArray
- equivalent_operator(j)[source]#
equivalent operator in descending order in Jz.
- Parameters:
j (str) -- magnitude of angular momentum, J (0, 1/2, 1, ...).
- Returns:
equivalent-operator matrix.
- Return type:
NSArray
- expression(v=None)[source]#
explicit expression of harmonics.
- Parameters:
v (NSArray, optional) -- vector variable to replace "[x,y,z]".
- Returns:
polynomial expression of harmonics.
- Return type:
NSArray
Notes
when v is None, default variable is used.
- to_vector()[source]#
cartesian vector for rank-1 expression.
- Returns:
converted cartesian vector.
- Return type:
NSArray
- u_matrix()[source]#
unitary matrix from (l,m) to the harmonics, \(X_{harm} = U^{\dagger}X_{lm}U\).
- Returns:
unitary matrix from (l,m) to the harmonics with (2l+1) components, descending order in m.
- Return type:
NSArray
- tag#
multipole tag.