3 research outputs found
ARBITRARY-ORDER HERMITE GENERATING FUNCTIONS FOR COHERENT AND SQUEEZED STATES
For use in calculating higher-order coherent- and squeezed- state quantities,
we derive generalized generating functions for the Hermite polynomials. They
are given by , for arbitrary
integers and . Along the way, the sums with the Hermite
polynomials replaced by unity are also obtained. We also evaluate the action of
the operators on well-behaved functions and apply them to
obtain other sums.Comment: LaTeX, 8 page
The Schr\"odinger system H=-{1/2}e^{\Upsilon(t-t_o)}\partial_{xx} +\lfrac{1}{2}\omega^2e^{-\Upsilon(t-t_o)}x^2
In this paper, we attack the specific time-dependent Hamiltonian problem
H=-{1/2}e^{\Upsilon(t-t_o)}\partial_{xx}
+\lfrac{1}{2}\omega^2e^{-\Upsilon(t-t_o)}x^2. This corresponds to a
time-dependent mass (TM) Schr\"odinger equation. We give the specific
transformations to i) the more general quadratic (TQ) Schr\"odinger equation
and to ii) a different time-dependent oscillator (TO) equation. For each
Schr\"odinger system, we give the Lie algebra of space-time symmetries, the
number states, the coherent states, the squeezed-states and the time-dependent
, , (\Delta x)^2, (\Delta p)^2, and uncertainty product.Comment: Latex, 24 pages, including 3 figures and 8 tables. New title and
format for journal. Conclusion adde