The Superposition of Two Identical States: The Empty State

Abstract

In this paper we define and study a new class of states (the empty states). These states are the superposition of two identical states (self-superposition state). We defined three different representations of theses states, namely, the source, the operator, and the self-superposition representations. Then, we apply the empty state to an elementary example state and find its three different representations. We apply the empty state to Fock states and find an undetermined state. Then, we apply the empty state to the coherent state to produce the empty state of the coherent state (the EC state), and determine some of its mathematical, statistical and nonclassical properties.