Displaced squeezed number states: Position space representation, inner product, and some applications

For some applications the overall phase of a quantum state is crucial. For the so-called displaced squeezed number state (DSN), which is a generalization of the well-known squeezed coherent state, we obtain the position space representation with the correct overall phase, from the dynamics in a harmonic potential. The importance of the overall phase is demonstrated in the context of characteristic or moment generating functions. For two special cases the characteristic function is shown to be computable from the inner product of two different DSNs.