GROUP THEORY SYMBOL
GTCharProjectionOperator
GTCharProjectionOperator[classes,characters,function,arguments]
applies the character projection operator corresponding to an irreducible representation to a certain function with given arguments.
Details
- The Projection operator
is given by 
, where 
is the dimension of the irreducible representation 
with characters 
and 
is the order of the group. - The characters
belong to an irreducible representation 
of the group 
. The classes and characters can be obtained using the command GTCharacterTable. - arguments is a list of arguments used by function, typically {x,y,z}
- The following option can be given:
-
GOFast False Controls the input validation GOLattice {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}} Gives the lattice vectors in case space groups are considered - See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 5.9
Examplesopen all
Basic Examples (3)
| In[1]:= |
For the example, the point group 
is considered. The point group and the character table are generated as follows:
The function 
will be analysed.
| In[4]:= |
The application of the character projection operator, related to the irreducible representation 
can be calculated by:
and for the irreducible representation 
by:
The same formalism holds for the irreducible representation 
,
GTCharProjectionOperator can also be used for 3-dimensional vector functions.
| In[1]:= |
If a double group is installed, GTCharProjectionOperator can be used for spinor functions.
| In[3]:= |
