"Nonclassical" states in quantum physics: brief historical review V. V Dodonov, V I Man'ko
V.V. Dodonov, V.I. Man'ko
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 \nin section 3). Lerner [120] noticed that the commutation relations (32) do not \ndetermine the operators C, S uniquely. Earlier, the same observation was made \nby Wigner [121] with respect to the triple {n, a, a*} (see the next section). In the \ngeneral case, besides the "polar decomposition" (31), which is equivalent to the \nrelations 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), \nwhere 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 \n"cosine" and "sine" operators belong to the interval (—1,1). The properties of \nLerner's construction were studied in [122].
CRC Press eBooks•Mar 13, 2003•1 citation