Construction of the Strong Coupling Expansion for the Ground State Energy of the Quartic, Sextic, and Octic Anharmonic Oscillator via a Renormalized Strong Coupling Expansion

Influence of the lattice vibration on the properties of the magnetopolaron in the parabolic quantum dots (QDs) is studied by using the Huybrechts' linear combination operator and Lee–Low–Pines (LLP) transformation methods. The expressions for the vibration frequency and the ground-state energy of the magnetopolaron as functions of the confinement strength of the QDs, the magnetic field and temperature are derived under the strong and weak coupling, respectively. The results of the numerical calculations show that the changes of the vibration frequency and ground-state energy of the magnetopolaron with the confinement strength of the QDs, the magnetic field and temperature are different under different couplings. The vibration frequency and the ground-state energy of the weak-coupling magnetopolaron and the vibration frequency of the strong-coupling magnetopolaron will increase with increase of the confinement strength of the QDs and cyclotron frequency, the vibration frequency and ground-state energy of the strong-coupling magnetopolaron. However, the ground-state energy of the weak-coupling magnetopolaron will decrease with increase of the temperature. The dependence of the ground-state energy of the strong-coupling magnetopolaron on the confinement strength of the QDs and cyclotron frequency is strongly influenced by the temperature. The remarkable influence of the temperature on the ground-state energy of the magnetopolaron arises when the temperature is relatively higher.

Download Full-text

SECOND ORDER APPROXIMATION FOR OPTICAL POLARON IN THE STRONG COUPLING CASE

Modern Physics Letters B ◽

10.1142/s0217984995000437 ◽

1995 ◽

Vol 09 (08) ◽

pp. 485-498

Author(s):

N. N. BOGOLUBOV

Keyword(s):

Strong Coupling ◽

Ground State Energy ◽

Ground State ◽

State Energy ◽

Order Approximation ◽

Nonlinear Differential Equations ◽

Second Order ◽

Linear Type ◽

Second Order Approximation ◽

Coupling Case

Here we propose a method of constructing a second order approximation for ground state energy for a class of model Hamiltonian with linear type interaction on bose operators in the strong coupling case. For the application of the above method we have considered polaron model and propose constructing a set of nonlinear differential equations for definition ground state energy in the strong coupling case. We have considered also radial symmetry case.

Download Full-text

Degenerate trajectories and Hamiltonian envelopes in the method of self-similar approximations

Canadian Journal of Physics ◽

10.1139/p93-082 ◽

1993 ◽

Vol 71 (11-12) ◽

pp. 537-546 ◽

Cited By ~ 6

Author(s):

V. I. Yukalov ◽

E. P. Yukalova

Keyword(s):

Schrödinger Equation ◽

Ground State Energy ◽

Ground State ◽

Schrodinger Equation ◽

Approximate Calculation ◽

State Energy ◽

Anharmonic Oscillator ◽

New Techniques ◽

Self Similar ◽

Very High

We study two new techniques for the approximate calculation of the eigenvalues of the Schrödinger equation. These techniques are variants of the method of self-similar approximations suggested recently by one of the authors. We illustrate the ideas by an anharmonic oscillator problem. We show that the precision of the method can be very high. For example, the ground-state energy of an anharmonic oscillator can be calculated with an error not exceeding 0.07% for all anharmonicity parameters ranging from zero to infinity.

Download Full-text