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Journal of Physics A Mathematical and General

Orthonormalized eigenstates of the operator {(âf(hatn))}k(kgeq1) and their generation

Xiaoming Liu

Published Nov 30, 1999• 20 citations
Publisher

Abstract

The k orthonormalized eigenstates of the powers {(â f ( ))} k ( k 1) of the annihilation operator â f ( ) of f -oscillators are obtained and their properties are discussed. An alternative method to construct them is proposed, and the result shows that all of the eigenstates can be generated by a linear superposition of k f -coherent states.

DOI
10.1088/0305-4470/32/49/309

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The completeness of the k orthonormalized eigenstates of the operator (â f ( )) k ( k ⩾3) is investigated. We introduce a new kind of higher-order squeezing and an antibunching. The properties of the M th-order squeezing and the antibunching effect of the k states are studied. The result shows that these states may form a complete Hilbert space, and the M th-order ( M = ( n + 1/2) k ; n = 0,1,...) squeezing effects exist in all of the k states when k is even. There is an antibunching effect in all of the states. An alternative method for constructing the k states is proposed, and the result shows that all of them can be generated by linear superposition of the time-dependent nonlinear coherent states at different instants.