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 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

SELF-TRAPPING TRANSITION OF ACOUSTIC POLARON IN SLAB

2013 ◽  
Vol 27 (08) ◽  
pp. 1350050
Author(s):  
JUNHUA HOU ◽  
XIAOMING DONG ◽  
XIAOFENG DUAN
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Alkali Halides ◽  
2D Systems ◽  
Phonon Coupling ◽  
Length Unit ◽  
First Derivative ◽  
Electron Phonon Coupling ◽  
Self Trapping

Self-trapping transition of the acoustic polaron in slab is researched by calculating the polaron ground state energy and the first derivative of the ground state energy with respect to the electron–phonon coupling. It is indicated that the possibility of self-trapping transition for acoustic polaron in slab fall in between 3D and 2D systems. The electron may be self-trapped in slab systems of GaN , AlN and alkali halides, if the slab systems are thinner than one over ten of the length unit ℏ/mc.

THE PROPERTIES OF STRONG-COUPLING IMPURITY BOUND MAGNETOPOLARON IN AN ANISOTROPIC QUANTUM DOT

2011 ◽  
Vol 25 (26) ◽  
pp. 3485-3494 ◽  
Author(s):  
WEI XIAO ◽  
JING-LIN XIAO
Keyword(s):  
Binding Energy ◽  
Ground State Energy ◽  
Ground State ◽  
Coupling Strength ◽  
Vibrational Frequency ◽  
State Energy ◽  
Cyclotron Frequency ◽  
Ground State Binding Energy ◽  
Electron Phonon Coupling ◽  
Increasing Function

We study the vibrational frequency, the ground-state energy and the ground-state binding energy of the strong-coupling impurity bound magnetopolaron in an anisotropic quantum dot. The effects of the transverse and longitudinal effective confinement lengths, the electron–phonon coupling strength, the cyclotron frequency of a magnetic field and the Coulomb bound potential are taken into consideration by using an linear combination operator and unitary transformation methods. It is found that the vibrational frequency, the ground-state energy and the ground-state binding energy will increase rapidly with decreasing confinement lengths. The vibrational frequency is an increasing function of the Coulomb bound potential, the electron–phonon coupling strength and cyclotron frequency, whereas the ground-state energy is a decreasing function of the potential and coupling strength, and the ground-state binding energy is an increasing function of the potential and coupling strength. The ground-state energy and the ground-state binding energy increases with increasing cyclotron frequency.

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

Fock approximation to the large polaron in a magnetic field

1976 ◽  
Vol 54 (19) ◽  
pp. 1979-1989 ◽  
Author(s):  
Y. Lepine ◽  
D. Matz
Keyword(s):  
Magnetic Field ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Cylindrical Symmetry ◽  
Coupling Constants ◽  
The Novel ◽  
Phonon Coupling ◽  
Electron Phonon Coupling ◽  
Large Polaron

We study the large polaron ground state energy in the presence of a constant and uniform magnetic field within the Fock approximation. By use of a new trial spectrum we find a new upper bound to the ground state energy for all magnetic fields and electron–phonon coupling constants. The trial spectrum has the novel feature of keeping cylindrical symmetry for certain values of coupling, even in the absence of magnetic field.

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.

scholarly journals Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution

2017 ◽  
Vol 3 (1) ◽  
Author(s):  
Guillaume Lang ◽  
Frank Hekking ◽  
Anna Minguzzi
Keyword(s):  
Excitation Spectrum ◽  
Series Expansion ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Interaction Strength ◽  
Exact Result ◽  
Mathematical Structure ◽  
Strong Interactions ◽  
Wide Range

We study the ground-state properties and excitation spectrum of the Lieb-Liniger model, i.e. the one-dimensional Bose gas with repulsive contact interactions. We solve the Bethe-Ansatz equations in the thermodynamic limit by using an analytic method based on a series expansion on orthogonal polynomials developed in and push the expansion to an unprecedented order. By a careful analysis of the mathematical structure of the series expansion, we make a conjecture for the analytic exact result at zero temperature and show that the partially resummed expressions thereby obtained compete with accurate numerical calculations. This allows us to evaluate the density of quasi-momenta, the ground-state energy, the local two-body correlation function and Tan’s contact. Then, we study the two branches of the excitation spectrum. Using a general analysis of their properties and symmetries, we obtain novel analytical expressions at arbitrary interaction strength which are found to be extremely accurate in a wide range of intermediate to strong interactions.

Sign in / Sign up

Export Citation Format

Share Document