Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian

Details Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian

2010-12-03

arxiv.org/abs/1012.0741v1

Physics

Quantum Physics

6 pages, 2 figures

Scientific paper

Based on the technique of integration within an ordered product (IWOP) of operators we introduce the Fresnel operator for converting Caldirola-Kanai Hamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresnel operator with the parameters A,B,C,D corresponds to classical optical Fresnel transformation, these parameters are the solution to a set of partial differential equations set up in the above mentioned converting process. In this way the exact wavefunction solution of the Schr\"odinger equation governed by the Caldirola-Kanai Hamiltonian is obtained, which represents a squeezed number state. The corresponding Wigner function is derived by virtue of the Weyl ordered form of the Wigner operator and the order-invariance of Weyl ordered operators under similar transformations. The method used here can be suitable for solving Schr\"odinger equation of other time-dependent oscillators.

Affiliated with

Also associated with

No associations

Rating

Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-515214