Transformation Theory

Abstract

In our example of the diagonalization of the asymmetric rotator Hamiltonian in the last chapter, we encountered a very special case of a very general problem in quantum theory, the transformation from one basis in Hilbert space to another. In our example, it was a transformation from the |J M K〉 basis to the |J M E _α〉 basis, involving two different complete sets of commuting operators to specify the two different bases. In our specific example of the J = 1 energy eigenstates, the transformation was a very simple one, in a 3-D subspace of the asymmetric rotator subspace of the full Hilbert space of our problem, and thus it involved a 3 × 3 transformation.