Smith, T.B.
(2006).
Generalized Qfunctions.
Journal of Physics A: Mathematical and General, 39(44) pp. 13747–13756.
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Abstract
The modulus squared of a class of wavefunctions defined on phase space is used to define a generalized family of Q or Husimi functions. A parameter lambda specifies orderings in a mapping from the operator psi)(sigma to the corresponding phase space wavefunction, where sigma is a given fiducial vector. The choice lambda = 0 specifies the Weyl mapping and the Qfunction so obtained is the usual one when sigma is the vacuum state. More generally, any choice of of lambda in the range (1,1) corresponds to orderings varying between standard and antistandard. For all such orderings the generalized Qfunctions are nonnegative by construction. They are shown to be proportional to expectation of the system state rho with respect to a generalized displaced squeezed state which depends on lambda and position (p,q) in phase space. Thus, when a system has been prepared in the state rho, a generalized Qfunction is proportional to the probability of finding it in the generalized squeezed state. Any such Qfunction can also be written as the smoothing of the Wigner function for the system state rho by convolution with the Wigner function for the generalized squeezed state.
Item Type: 
Journal Article

ISSN: 
17518121 
Extra Information: 
Some of the symbols may not have transferred correctly into this bibliographic record and/or abstract. 
Keywords: 
Wigner function; Q function; Weyl correspondence; squeezed state 
Academic Unit/Department: 
Science > Physical Sciences Science 
Item ID: 
5859 
Depositing User: 
Tom Smith

Date Deposited: 
14 Nov 2006 
Last Modified: 
14 Jan 2016 18:58 
URI: 
http://oro.open.ac.uk/id/eprint/5859 
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