ABSTRACT
COHERENT AND " N O N C L A S S I C A L " STATES 3
4 BRIEF HISTORY OF NONCLASSICAL STATES
COHERENT AND " N O N C L A S S I C A L " STATES 5
6 BRIEF HISTORY OF NONCLASSICAL STATES
CHILDHOOD OF SQUEEZED STATES 7
8 BRIEF HISTORY OF NONCLASSICAL STATES
COHERENT STATES OF NONSTATIONARY OSCILLATORS 9
NON-GAUSSIAN OSCILLATOR STATES 11
12 BRIEF HISTORY OF NONCLASSICAL STATES
COHERENT PHASE STATES 13
in the last decade of the 20th century (see the paragraph on photon-added states in section 3). Lerner [120] noticed that the commutation relations (32) do not determine the operators C, S uniquely. Earlier, the same observation was made by Wigner [121] with respect to the triple {n, a, a*} (see the next section). In the general case, besides the "polar decomposition" (31), which is equivalent to the relations
E-\n) = (1-Sn0)\n - 1), E+\n) = |n + 1), (35)
one can define operator U = C + iS via the relation U\n) = f(n)\n -1), where function f(n) may be arbitrary enough, being restricted by the requirement /(0) =0 and certain other constraints which ensure that the spectra of the "cosine" and "sine" operators belong to the interval (—1,1). The properties of Lerner's construction were studied in [122].
