Classical and quantum approach to Davydov’s soliton theory

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Abstract
A method introduced by Davydov for modeling energy transport in deformable molecular chains is considered, using for the ansatz function a superposition of tensor products of single-exciton and coherent-phonon states. Treating the time-dependent parameters of the function (exciton and phonon amplitudes) as generalized coordinates, we have shown that the corresponding Euler-Lagrange equations are consistent with the averaged quantum equations, although the ansatz function does not satisfy the Schrödinger equation. For the case of the immobile-exciton limit (in which the quantum-mechanical problem is exactly solvable), it is shown that the ansatz function satisfies the Schrödinger equation, so all predictions based on Davydov’s method are identical to the corresponding exact results (for this particular case).

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