Interacting Morse oscillators.
- From: kurdayon@xxxxxxxxx
- Date: 28 Apr 2005 01:43:06 -0700
Hi all,
I have the following potential energy which depends on two coordinates
(x1 and x2): V(x1,x2) = Morse(D1,alpha1,x1) + Morse(D2,alpha2,x2) +
beta*x1*x2,
where Morse(D,alpha,x) is well known Morse potential: Morse(D,alpha,x)
= D*(1-exp(-alpha*(x-x0)))^2. I would like to solve the Schroedinger
equation with this potential. My question is whether there is already
analytical solution for this system somewhere. If yes, where I can find
it? If not, how I need to handle this system?
What I found is the following. We can express express parameters of
Morse potential (D and alpha) through new set of parameters (a and k).
D = 9/2*k^3/a^2, alpha = -1/3*a/k. And then if we take a=0 Morse
potential transforms to usual harmonic potential. In such way we obtain
a system of two harmonic interacting oscillators. So, for a=0 we have
analytical solution. The second partial case is beta=0. In this case we
have two not interacting Morse potentials which can be considered
independently and as a consequence we have analytical solution again.
But what one can do if both "a" and "beta" are not equal to zero. May
be one need to use perturbation theory with respect to these parameters?
.
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