Skip to main content
Log in

Time-dependent linear Hamiltonian systems and quantum mechanics

  • Published:
Letters in Mathematical Physics Aims and scope Submit manuscript

Abstract

In this Letter, a theorem on time-dependent linear Hamiltonian systems is recalled and its connection with the Schrödinger equation is discussed. The kernel of the evolution operator of such quantum systems is computed. Furthermore, the Lewis and Riesenfeld theory for systems with many degrees of freedom is generalized.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. CoppelW. A.: Disconjugacy, Lecture Notes in Math. 220, Springer, Berlin, 1971.

    Google Scholar 

  2. Rezende, J.: Explicit solutions for some linear Hamiltonian systems, Preprint BiBoS No. 636/5/94, Bielefeld, 1994.

  3. DittrichW. and ReuterM.: Classical and quantum Dynamics, Springer-Verlag, Berlin, 1994.

    Google Scholar 

  4. Lewis, H. R., Jr., and Riesenfeld, W. B.: An exact quantum theory of the time-dependent harmonic oscillator and a charged particle in a time-dependent electromagnetic field, J. Math. Phys. 10 (1969).

  5. HillJ. M.: Solution of Differential Equations by Means of One-Parameter Groups, Research Notes in Math. 63, Pitman, London, 1982.

    Google Scholar 

  6. MagnusW.: On the exponential solution of differential equations for a linear operator, Comm. Pure Appl. Math. 7 (1954), 649–673.

    Google Scholar 

  7. PechukasP. and LightJ. C.: On the exponential form of time-displacement operators in quantum mechanics, J. Chem. Phys. 44 (1966), 3897–3912.

    Google Scholar 

  8. RezendeJ.: Quantum systems with time-dependent harmonic part and the Morse index, J. Math. Phys. 25 (1984), 3264–3269.

    Article  Google Scholar 

  9. RezendeJ.: Feynman integrals and Fredholm determinants, J. Math. Phys. 35 (1994), 4357–4371.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rezende, J. Time-dependent linear Hamiltonian systems and quantum mechanics. Lett Math Phys 38, 117–127 (1996). https://doi.org/10.1007/BF00398314

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00398314

Mathematics Subject Classifications (1991)

Key words

Navigation