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The Isomorphic Groups D3, S3, C3v

Gamma

Cayley Tables




Specific Embodiments

D3 ImageS3 Group




Three non-interacting particles in an identical well.

Single particle levels enumerated by n. States, where {tuv}={123} = particle labels, organized so as to result in the regular representation ():

n

1

2

3

4

5

6

tuv

123

312

231

132

321

213

G4 Matrix

One of the six representation matrices of the altered scrutiny of permutation.

 

Find so the reduced matrix is
Reduced G

State has property , that any permutation returns the same state so if have bosons only one state is admissable; the one that transforms as γ=1.

State produces ±1 on even/odd permutation; fermions

Transformation matrix





The transformation matrix between irrep states, |γjk>, of the system and states, |n>, of the system






 

December 2014
Marvin Chester
email



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