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Davydov Ansatz and Proper Solutions of Schrödinger Equation for Fröhlich Hamiltonian

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Davydov’s Soliton Revisited

Part of the book series: NATO ASI Series ((NSSB,volume 243))

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Abstract

Theory of Davydov solitons in molecular systems is rather well established nowadays1, but certain problems dealing with the quantum-mechanical foundations of the theory still remain, especially those concerning the applicability of various equations of motion, both quantum and classical.

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References

  1. A.S. Davydov, Solitons in Molecular Systems (Solitony v molekulyarnyh sistemah), Naukova dumka, Kiev (1988) (in Russian).

    Google Scholar 

  2. H. Fröhlich, Electrons in Lattice Fields, Adv. Phys. 3, 325 (1954).

    Article  ADS  Google Scholar 

  3. A. Messiah, Quantum mechanics, Wiley, New York (1962).

    MATH  Google Scholar 

  4. A.S. Davydov, Dvizhenie solitona v odnomernoi molekulyarnoi reshetke s uchetom teplovih kolebanii, Zh. Eksp. Teor. Fiz. 78, 789 (1980) Sov. phys. — JETP 51, 397 (1980)].

    ADS  Google Scholar 

  5. D.W. Brown, K. Lindenberg and B.J. West, Applicability of Hamilton’s equations in the quantum soliton problem, Phys. Rev. B 33, 4104 (1986).

    MathSciNet  ADS  Google Scholar 

  6. D.W. Brown, B.J. West and K. Lindenberg, Davydov solitons: New results at variance with standard derivations, Phys. Rev. B 33, 4110 (1986).

    MathSciNet  ADS  Google Scholar 

  7. W.C. Kerr and P.S. Lomdahl, Quantum-mechanical derivation of the equations of motion for Davydov solitons, Phys. Rev. 35, 3629 (1987)

    Article  ADS  Google Scholar 

  8. D.W. Brown, Balancing the Schrödinger equation with Davydov Ansätze, Phys. Rev. A 37, 5010 (1988).

    Article  MathSciNet  ADS  Google Scholar 

  9. M.J. Škrinjar, D.V. Kapor and S. Stojanovic, Classical and quantum approach to Davydov’s soliton theory, Phys Rev. B 38, 6402 (1988).

    Article  Google Scholar 

  10. Q. Zhang, V. Romera-Rochin and R. Silbey, Variational approach to Davydov soliton, Phys. Rev, B38, 6409 (1988).

    ADS  Google Scholar 

  11. J.R. Klauder, The Action Option and a Feynman Quantization of Spinor Fields in Terms of Ordinary C-Numbers, Ann. of Phys. 11, 123 (1960).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. L.R. Mead and N. Papanicolaou, Holstein-Primakoff theory for many-body systems, Phys. Rev. B 28, 1633 (1983).

    Article  MathSciNet  ADS  Google Scholar 

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Škrinjar, M., Kapor, D., Stojanovic, S. (1990). Davydov Ansatz and Proper Solutions of Schrödinger Equation for Fröhlich Hamiltonian. In: Christiansen, P.L., Scott, A.C. (eds) Davydov’s Soliton Revisited. NATO ASI Series, vol 243. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9948-4_8

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  • DOI: https://doi.org/10.1007/978-1-4757-9948-4_8

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-9950-7

  • Online ISBN: 978-1-4757-9948-4

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