|
|
 |
| |
|
|
|
Generalization of the Mehler’s formula |
|
|
|
PP: 463-471 |
|
|
|
doi:10.18576/amis/180220
|
|
|
|
Author(s) |
|
|
|
Marco A. Tapia-Valerdi,
Ira ́n Ramos-Prieto,
Francisco Soto-Eguibar,
He ́ctor M. Moya-Cessa,
|
|
|
|
Abstract |
|
|
| We demonstrate that a generalization of the Mehler’s formula can be achieved by employing techniques commonly utilized in quantum optics. The methodology involves deriving the Mehler’s formula through the solution of a Schro ̈dinger-type equation. The selection of the initial conditions, determines the type of Mehler’s formula obtained; for example, the usual Mehler’s formula is obtained when the initial condition is the product of two harmonic oscillator base functions. In this article, we focus on investigating specific initial conditions that hold significance within the quantum optics community.
|
|
|
|
|
|
|
|
