Variational calculation of the ground-state energy of the bound polaron

1978 ◽  
Vol 27 (1) ◽  
pp. 45-47 ◽  
Author(s):  
W.J. Huybrechts
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Variational Calculation ◽  
Bound Polaron

TEMPERATURE-DEPENDENCE OF STRONG-COUPLED BOUND POLARON IN A TRIANGULAR POTENTIAL QUANTUM DOT

2012 ◽  
Vol 26 (03) ◽  
pp. 1150015 ◽  
Author(s):  
ZHI-XIN LI
Keyword(s):  
High Temperature ◽  
Quantum Dot ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Polar Angle ◽  
Strongly Coupled ◽  
Influence Of Temperature ◽  
Leading Role ◽  
Bound Polaron

We study the temperature effect of bound polaron, which is strongly coupled to LO-phonon by using a variational method of the Pekar type in a triangular potential quantum dot (QD). The ground state energy was expressed as functions of the confinement length of QD, the Coulomb bound potential, the polar angle and the temperature. It is found that at low temperature, the influence of Coulomb bound potential and the confinement length of QD to the ground state energy of bound polaron play a leading role. At high temperature, the influence of temperature to the ground state energy of bound polaron is dominant.

Variational calculation on ground-state energy of bound polarons in parabolic quantum wires

2001 ◽  
Vol 10 (5) ◽  
pp. 437-442 ◽  
Author(s):  
Wang Zhuang-bing ◽  
Wu Fu-li, Chen Qing-hu ◽  
Jiao Zheng-kuan
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Quantum Wires ◽  
Variational Calculation

BINDING ENERGY OF A BOUND POLARON IN THE FINITE PARABOLIC QUANTUM WELL

2001 ◽  
Vol 15 (20) ◽  
pp. 827-835 ◽  
Author(s):  
FENG-QI ZHAO ◽  
XI XIA LIANG
Keyword(s):  
Binding Energy ◽  
Quantum Well ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Transition Energy ◽  
Energy Levels ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Bound Polaron

We have studied the effect of the electron–phonon interaction on the energy levels of the bound polaron and calculated the ground-state energy, the binding energy of the ground state, and the 1 s → 2 p ± transition energy in the GaAs/Al x Ga 1-x As parabolic quantum well (PQW) structure by using a modified Lee–Low–Pines (LLP) variational method. The numerical results are given and discussed. It is found that the contribution of electron–phonon interaction to the ground-state energy and the binding energy is obvious, especially in large well-width PQWs. The electron–phonon interaction should not be neglected.

Ground State Energy of Polaron Bound in a Coulomb Potential

1974 ◽  
Vol 52 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Mitsuru Matsuura
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
Present Method ◽  
State Energy ◽  
Variational Calculation ◽  
Effective Potentials ◽  
Important Region ◽  
Electron Phonon Coupling ◽  
Wide Range ◽  
Path Integral Method

The path integral method is used to obtain an expression, involving a sum over the complete set of solutions for the effective trial Hamiltonian, for the ground state energy of the bound polaron. The numerical calculations of this expression are performed for the hydrogenic and harmonic oscillator effective potentials. The present method together with several previous theories and their numerical results are discussed over a wide range of the electron–phonon coupling constant α and the electron–massive hole coupling β. It is shown that, for the experimentally important region, the present method with the hydrogenic potential yields the lowest energy—slightly lower than obtained by the Larsen's variational calculation.

Variational calculation of ground-state energy of iron atoms and condensed matter in strong magnetic fields

1977 ◽  
Vol 215 ◽  
pp. 291 ◽  
Author(s):  
E. G. Flowers ◽  
M. A. Ruderman ◽  
J.-F. Lee ◽  
P. G. Sutherland ◽  
W. Hillebrandt ◽  
...  
Keyword(s):  
Magnetic Fields ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Condensed Matter ◽  
Variational Calculation ◽  
Strong Magnetic Fields

Bound state for a screened impurity in a magnetic field

1978 ◽  
Vol 56 (7) ◽  
pp. 913-916 ◽  
Author(s):  
S. D. Jog
Keyword(s):  
Magnetic Field ◽  
Wave Function ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Spherical Wave ◽  
Bound State ◽  
Variational Calculation ◽  
Coulomb Wave Function ◽  
Spherical Part

A variational calculation of the ground state energy of an electron bound to a screened impurity in a semiconductor in a magnetic field is presented. The trial wave function is taken to be a product of a Landau wave function and a spherical wave function. We consider and compare the two cases in which the spherical part is chosen to be (i) a Coulomb wave function (after Rau, Mueller, and Spruch) and (ii) a Hulthén wave function.

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