The Trajectory-coherent Approximation and the System of Moments for the Hartree Type Equation

@inproceedings{BELOV2000TheTA,
  title={The Trajectory-coherent Approximation and the System of Moments for the Hartree Type Equation},
  author={A. YU. TRIFONOV V. V. BELOV and Alexander V. Shapovalov},
  year={2000}
}
The general construction of quasi-classically concentrated solutions to the Hartree type equation, based on the complex WKB–Maslov method, is presented. The formal solutions of the Cauchy problem for this equation, asymptotic in small parameter ~ (~→ 0), are constructed with a power accuracy of O(~), where N is any natural number. In constructing the quasi-classically concentrated solutions, a set of Hamilton– Ehrenfest equations (equations for centered moments) is essentially used. The… CONTINUE READING

Citations

Publications citing this paper.
Showing 1-10 of 12 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 49 references

Semiclassical Trajectory-coherent Approximation in Quantum Mechanics: I. High Order Corrections to Multidimensional Time-dependent Equations of Schrödinger Type

  • V. G. Bagrov, V. V. Belov, A.Yu. Trifonov
  • Ann. of Phys. (NY),
  • 1996
Highly Influential
8 Excerpts

Generalized Coherent States and Their Application

  • A. M. Perelomov
  • Berlin, Springer-Verlag
  • 1986
Highly Influential
12 Excerpts

Dynamic Symmetries and Coherent States of Quantum Systems

  • M. A. Malkin, V. I. Manko
  • Moscow, Nauka
  • 1979
Highly Influential
16 Excerpts

A System with a Quadric Hamiltonian Written as a Time-dependent Quadric Form of x̂ and p̂

  • N. A. Chernikov
  • – Zh. Eksper. Teor. Fiz.
  • 1967
Highly Influential
14 Excerpts

The Quantum Theory of Optical Coherence

  • R. J. Glauber
  • – Phys. Rev.
  • 1963
Highly Influential
12 Excerpts

On the Mathematical Foundation of Quantum Electrodynamics

  • P. K. Rashevsky
  • – Usp. Mat. Nauk
  • 1958
Highly Influential
12 Excerpts

Der stetige Übergang von der Mikro- zur Makromekanik

  • E. Schrödinger
  • Naturwissenschaften
  • 1926
Highly Influential
12 Excerpts

Localized Asymptotical Solutions to the Hartree Type Equation with a Gaussian Potential

  • G. N. Serezhnikov, A.Yu. Trifonov, A. V. Shapovalov
  • Izv. Tomsk State University,
  • 2000
1 Excerpt

Shapovalov, Quasi-classical Trajectory-coherent Approximation for the Hartree Type Equation

  • V. D. Baranov, V. V. Belov, A.Yu. Trifonov, A.V
  • Proc. Int. Summer School on Modern Problems of…
  • 2000
1 Excerpt

Shapovalov, The Hamilton-Ehrenfest System and Hartree Type Equations

  • V. V. Belov, G. N. Serezhnikov, A.Yu. Trifonov, A.V
  • Proc. Int. Conf. on Symmetry and Differential…
  • 2000
1 Excerpt

Similar Papers

Loading similar papers…