Symmetry of the Wave Functions (エルゴ-ド理論とその周辺)

Takeyuki Hida

信彦 斎藤

Akiva Novoselsky, Jacob Katriel

The weights of the different permutational symmetry components of a nonsymmetry-adapted many-particle wave function are evaluated in terms of the expectation values of the symmetric-group class sums. This facilitates the evaluation of the weights without the construction of a complete set of symmetry adapted functions. Subspace projection operators are introduced, to be used when prior knowledge about the symmetry-species composition of a wave function is available. The permutational weight analysis of a recursively angular-momentum coupled (shell model) wave function is presented as an illustration.

Sudin Singh, Ankabehari Saha

In this paper, the plane wave solutions of a free particle in three dimensions for Cubical and Spherical Symmetry have been considered. The coordinate space wave functions for the Cubical and Spherical Symmetry are obtained by solving the Schrdinger differential equation. The momentum space wave function is obtained by using the operator form of an observable in the case of Cubical Symmetry. For Spherical Symmetry, the same is obtained by taking the Fourier transform of the respective coordinate space wave function. The wave functions have been used to constitute probability densities in coordinate and momentum space for both the symmetries. Further, the Shannon information entropy has been computed both in coordinate and momentum space respectively for (L is the length of the side of the cubical box) values for Cubical Symmetry and for values in Spherical Symmetry keeping (k is the wave vector and p is the momentum of the free particle) constant. The values obtained for the Shannon information entropies are found to satisfy the Bialynicki-Birula and Myceilski (BBM) inequality at larger values () in case of Cubical Symmetry and for values of and in Spherical Symmetry.

Rhett J. Allain