Stretched Coherent States

The fundamental properties of recently introduced stretched coherent states are investigated. It has been shown that stretched coherent states retain the fundamental properties of standard coherent states and generalize the resolution of unity, or completeness condition, and the probability distribution that $n$ photons are in a stretched coherent state. The stretched displacement and stretched squeezing operators are introduced and the multiplication law for stretched displacement operator is established. The results of the action of the stretched displacement and stretched squeezing operators on the vacuum and the Fock states are presented. Stretched squeezed stretched coherent states and stretched squeezed stretched displaced number states are introduced and their properties are studied. The inner product of two quantum mechanical vectors was defined in terms of their stretched coherent state representations, and functional Hilbert space was introduced.