TY - JOUR
T1 - Squeezed states, generalized Hermite polynomials and pseudo-diffusion equation
AU - Mizrahi, Salomon S.
AU - Daboul, Jamil
N1 - Funding Information:
l With partial support from CNPq, Brazil. 2 E-mail: [email protected], subject: Salomon. 3 On sabbatical leave from the Physics Department, Ben-Gurion University of the Negev, Beer Sheva, Israel.
PY - 1992/11/1
Y1 - 1992/11/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0008464467&partnerID=8YFLogxK
U2 - 10.1016/0378-4371(92)90066-Y
DO - 10.1016/0378-4371(92)90066-Y
M3 - Article
AN - SCOPUS:0008464467
SN - 0378-4371
VL - 189
SP - 635
EP - 650
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 3-4
ER -