Eigenstates and operators

Daniel M. Greenberger, Klaus Hentschel, Friedel Weinert

Xuefen Xu

The paper studies the eigenstate of the inverse operators a-1 and (a+)-1 in Fock space, then educes the eigenstate of inverse operator a-1 and the eigenstate of inverse operator (a+)-1 is zero.

Marian J. R. Gilton

Gabino Torres-Vega

The usual method for obtaining the eigenstates of an operator is to solve the corresponding eigenvalue equation. This procedure cannot be applied when the operator of interest is not known at all. We develop a method which generates the eigenstates of an operator, and the operator itself, which will be conjugate to a given known operator. This is particularly useful for the case of the time operator in Quantum Mechanics. We illustrate the method by obtaining time eigenstates for the free particle.

G. M. Saxena, C. L. Mehta, B.S. Mathur

The inverse of paraboson annihilation and creation operators is introduced. The properties of these operators, their number state representation and commutation relations are discussed. Also introduced are the family of eigenstates of bilinears in paraboson operators and their inverses; and study the nonclassical properties, namely, squeezing and fluctuations in number of parabosons in these eigenstates. It is observed that a family of the eigenstates of a+−1a is the parasqueezed vacuum, S(σ)‖0,α〉. Similarly, a family of the eigenstates of aa+−1 is the parasqueezed first state, S(σ)‖n=1,α〉.

Brian L. Silver