Squeezed states, generalized Hermite polynomials and pseudo-diffusion equation

Salomon S. Mizrahi, Jamil Daboul

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

We show that the wavefunctions 〈pq; λ|n〈, of the harmonic oscillator in the squeezed state representation, have the generalized Hermite polynomials as their natural orthogonal polynomials. These wavefunctions lead to generalized Poisson Distribution Pn(pq;λ), which satisfy an interesting pseudo-diffusion equation: ∂Pnp,q;λ) ∂λ= 1 4 [ ∂2 ∂p2-( 1 λ2) ∂2 ∂q2]P2(p,q;λ), in which the squeeze parameter λ plays the role of time. Th entropies Sn(λ) have minima at the unsqueezed states (λ=1), which means that squeezing or stretching decreases the correlation between momentum p and position q.

Original languageEnglish
Pages (from-to)635-650
Number of pages16
JournalPhysica A: Statistical Mechanics and its Applications
Volume189
Issue number3-4
DOIs
StatePublished - 1 Nov 1992
Externally publishedYes

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