Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 1 (2005), 003, 9 pages      quant-ph/0511212      http://dx.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.

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References

  1. Feynman R.P., Space-time approach to non-relativistic quantum mechanics, Rev. Mod. Phys., 1948, V.20, 367-387.
  2. Grosche C., Steiner F., Handbook of Feynman path integrals, Springer Tracts in Modern Physics, V.145, Berlin, Springer-Verlag, 1998.
  3. Moshinsky M., Diffraction in time, Phys. Rev., 1952, V.88, 625-631.
  4. Moshinsky M., Quesne C., Linear transformations and their unitary representation, J. Math. Phys., 1971, V.12, 1772-1780.
  5. Gradshteyn I.S., Ryzhik I.M., Tables of integrals, series and products, New York - London, Academic Press, 1965.

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