By Frechette V.D.
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Extra info for Non-Crystalline Solids
As we have shown in the previous chapter, the eigenvalues are Thus, the space inversion transformation shows us that the eigenfunctions of the Schrijdinger equation can be scalar or pseudoscalar functions. 14b) that under space inversion transformation the electromagnetic field potentials are transformed in the following way A ( I ) = A ( r )= A (r) , cp' (r') = cp' (-r) = cp (r). 14) we transform these equation to their initial unprimed form. 14) is invariant with respect to the space inversion transformation.
The second difference is in the fact that the equations for interacting particles, along with the particle equations, should include the equation for the fields realizing the interaction. 12) could not coincide with the symmetry properties of the particle wave equations. Therefore the symmetry properties of the equation for single particle can be significantly different from the symmetry properties of equations for an ensemble of interacting particles. Let us consider the spatial transformations.
The state in which the wave function does not change its sign is called by the even state, if the wave function changes its sign under the space inversion transformation then the corresponding state is called by the odd state. Thus the invariance of the Harniltonian with respect to the space inversion transformation manifests the parity conservation law: if an isolated ensemble of particles has a definite parity, then the parity remains invariable in the process of ensemble evolution. The wave functions of the even states are the scalar functions, the wave functions of the odd states are the pseudoscalar functions.