Higher-power coherent and squeezed states

Abstract A closed form expression for the higher-power coherent states (eigenstates of a j ) is given. The cases j =3,4 are discussed in detail, including the time-evolution of the probability densities. These are compared to the case j =2, the even- and odd-coherent states. We give the extensions to the “effective” displacement-operator, higher-power squeezed states and to the ladder-operator/minimum-uncertainty, higher-power squeezed states. The properties of all these states are discussed.