Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics C Solid State Physics

A non-perturbative approach to the bound polaron. II

S. Mukhopadhyay, Tapas Mitra

Published Jun 20, 1980• 6 citations
Publisher

Abstract

For pt.I see Phys. Lett. A, vol.71, p.385 (1979). A recently developed non-perturbative iterative variational method has been applied to the bound polaron problem. The electron-phonon Hamiltonian is reduced in successive orders resulting in a transformed electronic Hamiltonian which gets an attractive phonon-induced potential from each order of reduction. The transformed electronic Hamiltonian has been solved numerically for a series of values of the parameters alpha , beta . Relation to perturbative solutions is discussed. Interesting localisation criteria derived from the calculated wavefunctions are also discussed.

DOI
10.1088/0022-3719/13/17/011

Related papers

A non-perturbative approach to the bound polaron. III

S. Mukhopadhyay, Tapas Mitra

For pt.II see ibid., vol.13, p.3193 (1980). The formal difficulties of the non-perturbative iteration variational method proposed recently for the ground state of the bound polaron problem are removed by a rigorous method of canonical transformation which not only yields essentially equivalent results but also extends its validity to excited states.

Journal of Physics C Solid State Physics•Feb 20, 1981•8 citations

Energy of a polaron bound to a Coulomb potential

Ward Huybrechts, G. Remaut

A variational calculation of the ground state and of the first excited state of a bound polaron is given for all values of the electron-phonon coupling and of the Coulomb potential. The applied unitary transformation formalism is adapted in order to take account of correlation between the longitudinal optical phonons.

physica status solidi (a)•Jun 16, 1980•6 citations

A Theory for the Bound Polaron. I. Wave Function

Katsuhiko Takegahara, T. Kasuya

Based on the unitary transformation, a general treatment of the bound polaron is proposed. In distinction from earlier calculations, the present method gives explicit expressions for not only the energy but also the wave functions both in the ground state and in the excited states such as the relaxed excited state and the phonon scattering state. These expressions involve a summation on the complete set of eigenstates of a trial Hamiltonian, and in actual calculations the Coulomb Hamiltonian and the harmonic oscillator Hamiltonian are chosen as trial Hamiltonians. For the ground state, the energy expression is the same as that obtained by Matsuura with the path integral method. The present method is valid in the whole region of the electron-phonon coupling constant α and Coulomb force β except for β→0 and α>6.

Journal of the Physical Society of Japan•Nov 1, 1975•36 citations

Phonon-Polaron Problem

Francis R. Halpern

The method of moments is employed to determine the ground state of the phonon-polaron system. The trial function employed in this calculation is a bare-electron wave function. It appears that the method is convergent for this problem. Although the energy is in general a complicated function of the parameter and must be determined numerically, it is possible to formally construct a power series expansion for the energy about the unperturbed energy in powers of the coupling constant. The first term in this series has been determined and agrees with the result of conventional perturbation theory. The second term has not yet been evaluated to all orders but it appears that it will have the opposite sign from the corresponding term in perturbation theory. The second and higher terms in some orders of approximation are singular for small values of the cutoff.

Physical Review•Mar 1, 1958•3 citations

The optical polaron bound in a Coulomb potential and its phase diagram

Naoaki Tokuda, H Shoji, K Yoneya

The optical polaron bounded in a Coulomb potential is investigated within the modified variational scheme of the Lee-Low-Pines theory (1953) which is valid for the whole range of the electron-phonon coupling. The ground state energy, the mean number of phonons in the cloud around the electron and the spatial localisation of the electron for the optical polaron change abruptly at certain values of the electron-phonon coupling constant alpha and of the Coulomb potential beta . The polaron changes its state according to the values of the parameters alpha and beta . Such features are summarised in the phase diagram.

Journal of Physics C Solid State Physics•Oct 20, 1981•19 citations

Two-site polaron problem: a perturbation approach with variational basis states

A. N. Das, Jayita Chatterjee

A convergent perturbation method using modified Lang Firsov transformation is developed for a two-site single-polaron system. The method is applicable for the entire range of the electron-phonon coupling strength. The single-electron energies, oscillator wave functions and correlation functions, calculated using this method, are in good agreement with the exact results. 2

•Jan 1, 1999•13 citations
For pt.I see Phys. Lett. A, vol.71, p.385 (1979). A recently developed non-perturbative iterative variational method has been applied to the bound polaron problem. The electron-phonon Hamiltonian is reduced in successive orders resulting in a transformed electronic Hamiltonian which gets an attractive phonon-induced potential from each order of reduction. The transformed electronic Hamiltonian has been solved numerically for a series of values of the parameters alpha , beta . Relation to perturbative solutions is discussed. Interesting localisation criteria derived from the calculated wavefunctions are also discussed.
Based on the unitary transformation, a general treatment of the bound polaron is proposed. In distinction from earlier calculations, the present method gives explicit expressions for not only the energy but also the wave functions both in the ground state and in the excited states such as the relaxed excited state and the phonon scattering state. These expressions involve a summation on the complete set of eigenstates of a trial Hamiltonian, and in actual calculations the Coulomb Hamiltonian and the harmonic oscillator Hamiltonian are chosen as trial Hamiltonians. For the ground state, the energy expression is the same as that obtained by Matsuura with the path integral method. The present method is valid in the whole region of the electron-phonon coupling constant α and Coulomb force β except for β→0 and α>6.
The method of moments is employed to determine the ground state of the phonon-polaron system. The trial function employed in this calculation is a bare-electron wave function. It appears that the method is convergent for this problem. Although the energy is in general a complicated function of the parameter and must be determined numerically, it is possible to formally construct a power series expansion for the energy about the unperturbed energy in powers of the coupling constant. The first term in this series has been determined and agrees with the result of conventional perturbation theory. The second term has not yet been evaluated to all orders but it appears that it will have the opposite sign from the corresponding term in perturbation theory. The second and higher terms in some orders of approximation are singular for small values of the cutoff.
The optical polaron bounded in a Coulomb potential is investigated within the modified variational scheme of the Lee-Low-Pines theory (1953) which is valid for the whole range of the electron-phonon coupling. The ground state energy, the mean number of phonons in the cloud around the electron and the spatial localisation of the electron for the optical polaron change abruptly at certain values of the electron-phonon coupling constant alpha and of the Coulomb potential beta . The polaron changes its state according to the values of the parameters alpha and beta . Such features are summarised in the phase diagram.