|
SIGMA 1 (2005), 003, 9 pages quant-ph/0511212
https://doi.org/10.3842/SIGMA.2005.003
Transient Phenomena in Quantum Bound States Subjected to a Sudden Perturbation
Marcos Moshinsky and Emerson Sadurní
Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Apartado Postal 20-364, 01000 Mexico D.F., Mexico
Received June 24, 2005, in final form August 08, 2005;
Published online August 18, 2005
Abstract
Transient phenomena in quantum mechanics have been
of interest to one of the authors (MM) since long ago and, in this paper,
we focus on the problem of a potential V- which for negative
times gives rise to bound states and is suddenly changed at t =
0 to a potential V+ which includes V-
plus a perturbed term. An example will be the deuteron (where the proton
and neutron are assumed to interact through an oscillator potential) submitted
to a sudden electrostatic field. The analysis for t >0 can be carried
out with the help of appropriate Feynmann propagators and we arrive at
the result that the separation between the nucleons has an amplitude that
depends on the intensity of the electrostatic field, but its period continues
to be related with the inverse of the frequency of the oscillator proposed
for the interaction. A general approximate procedure for arbitrary problems
of this type is also presented at the end.
Key words:
transient phenomena; propagators.
pdf (196 kb)
ps (148 kb)
tex (12 kb)
References
- Feynman R.P., Space-time approach to
non-relativistic quantum mechanics, Rev. Mod. Phys., 1948, V.20,
367-387.
- Grosche C., Steiner F., Handbook of Feynman path
integrals, Springer Tracts in Modern Physics, V.145, Berlin, Springer-Verlag, 1998.
- Moshinsky M., Diffraction in time, Phys. Rev., 1952, V.88, 625-631.
- Moshinsky M., Quesne C., Linear transformations
and their unitary representation, J. Math. Phys., 1971, V.12, 1772-1780.
- Gradshteyn I.S., Ryzhik I.M., Tables of
integrals, series and products, New York - London, Academic Press, 1965.
|
|