Calculation of the ground-state energy and studies of other properties of exotic helium atoms with the use of boundary conditions of wave function

2004 ◽  
Vol 101 (3) ◽  
pp. 320-324 ◽  
Author(s):  
M. R. Eskandari ◽  
B. Rezaie
Keyword(s):  
Wave Function ◽  
Boundary Conditions ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Helium Atoms

Liquid 4He: Equation of State, Compressibility and Velocity of First Sound

1998 ◽  
Vol 12 (21) ◽  
pp. 2115-2127 ◽  
Author(s):  
B. Skjetne ◽  
E. Østgaard
Keyword(s):  
Wave Function ◽  
Equation Of State ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Experimental Results ◽  
Interaction Models ◽  
First Sound ◽  
Polynomial Expression ◽  
Theoretical Results

In calculations for liquid 4 He , an investigation is made to check the accuracy of a lowest-order constrained variational (LOCV) method, using modified "healing" conditions on the two-body Jastrow wave function. Results obtained for the ground-state energy for four different interaction models are fitted by a polynomial expression, whereby the pressure, compressibility and velocity of first sound are obtained. The theoretical results are found to be in fair agreement with experimental results.

EXCITON IN ZnO FILM

2007 ◽  
Vol 21 (31) ◽  
pp. 5237-5245 ◽  
Author(s):  
HUA ZHAO ◽  
WEN XIONG ◽  
MENG-ZAO ZHU
Keyword(s):  
Wave Function ◽  
Film Thickness ◽  
Effective Mass ◽  
Ground State Energy ◽  
Ground State ◽  
Quantum Tunneling ◽  
State Energy ◽  
Zno Film ◽  
Mass Approximation ◽  
Exciton Wave Function

The present study variationally calculates the ground state energy and the first excited energy of an exciton in an ZnO film in effective mass approximation. Change of the ground state energy, the first excited energy of an exciton, and radius of the exciton with film thickness are studied, as well as the correction due to the quantum tunneling of the exciton wave function through the film.

scholarly journals Electronic States in a Doubly Eccentric Cylindrical Quantum Wire

2020 ◽  
Vol 12 (4) ◽  
pp. 473-483
Author(s):  
R. Kumar ◽  
S. N. Singh
Keyword(s):  
Boundary Conditions ◽  
Effective Mass ◽  
Ground State Energy ◽  
Ground State ◽  
Quantum Wire ◽  
State Energy ◽  
Electronic States ◽  
Addition Theorem ◽  
Limiting Behavior ◽  
Soft Wall

Electronic states of a single electron in doubly eccentric cylindrical quantum wire are theoretically investigated in this paper. The motion of electron in quantum wire is free along axial direction in a cylindrical quantum wire and restricted in annular regions by three different parallel finite cylindrical barriers as soft wall confinement. The effective mass Schrödinger equation with effective mass boundary conditions is used to find energy eigenvalues and   corresponding wavefunctions. Addition theorem for cylindrical Bessel functions is used to shift the origin for applying boundary conditions at different circular boundaries. Fourier expansion is applied after addition theorem to get wavefunctions in analytical form. A determinant equation is obtained as a result of applications of effective mass boundary conditions which roots gives energy of various electronic states. The lowest root gives ground state energy. The variation in ground state energy with eccentricity is obtained numerically and presented graphically. Electronic states in massive wall confinement and hard wall confinement is further obtained as limiting behavior of the states obtained in soft wall confinement. The knowledge of electronic states in such cylindrical hetrostructures semiconductor material can lead to improve the efficiency of many quantum devices.

scholarly journals Variational Principle Techniques and the Propertiesof a Cut-off and Anharmonic Wave Function

2009 ◽  
Vol 6 (1) ◽  
pp. 113-119 ◽  
Author(s):  
A. N. Ikot ◽  
L. E. Akpabio ◽  
K. Essien ◽  
E. E. Ituen ◽  
I. B. Obot
Keyword(s):  
Dynamical System ◽  
Wave Function ◽  
Variational Principle ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Variational Principles ◽  
Analytical Tool ◽  
Three Dimensions ◽  
Anharmonic Oscillators

The variational principles are very useful analytical tool for the study of the ground state energy of any dynamical system. In this work, we have evaluated the method and techniques of variational principle to derive the ground state energy for the harmonic, cut-off and anharmonic oscillators with a ground state wave function for a one-body Hamiltonian in three dimensions.

STUDY OF THE EXCITED STATE OF DOUBLE-Λ HYPERNUCLEI BY HYPERSPHERICAL SUPERSYMMETRIC APPROACH

2001 ◽  
Vol 10 (02) ◽  
pp. 107-127 ◽  
Author(s):  
MD. ABDUL KHAN ◽  
TAPAN KUMAR DAS ◽  
BARNALI CHAKRABARTI
Keyword(s):  
Wave Function ◽  
Excited State ◽  
Schrödinger Equation ◽  
Ground State Energy ◽  
Ground State ◽  
Schrodinger Equation ◽  
State Energy ◽  
First Excited State ◽  
Three Body ◽  
Partner Potential

Hyperspherical harmonics expansion (HHE) method has been applied to study the structure and ΛΛ dynamics for the ground and first excited states of low and medium mass double-Λ hypernuclei in the framework of core+Λ+Λ three-body model. The ΛΛ potential is chosen phenomenologically while core-Λ potential is obtained by folding the phenomenological Λ N interaction into the density distribution of the core. The parameters of this effective Λ N potential is obtained by the condition that they reproduce the experimental (or empirical) data for core-Λ subsystem. The three-body (core+Λ+Λ) Schrödinger equation is solved by hyperspherical adiabatic approximation (HAA) to get the ground state energy and wave function. This ground state energy and wave function are used to construct a partner potential. The three-body Schrödinger equation is solved once again for this partner potential. According to supersymmetric quantum mechanics, the ground state energy of this potential is exactly the same as that of the first excited state of the potential used in the first step. In addition to the two-Λ separation energy for the ground and first excited state, some geometrical quantities for the ground state of double-Λ hypernuclei [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are computed. These include the ΛΛ bond energy and various r.m.s. radii.

GENERALIZED GUTZWILLER ANSATZ FOR THE HALF-FILLED HUBBARD CHAIN

1988 ◽  
Vol 02 (05) ◽  
pp. 1021-1034 ◽  
Author(s):  
Patrik Fazekas ◽  
Karlo Penc
Keyword(s):  
Wave Function ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Occupation Number ◽  
Step Function ◽  
Spin Correlations ◽  
One Dimensional ◽  
Leading Term ◽  
The One

The well-known Gutzwiller wave function is generalized by including new variational parameters to control nearest-neighbour charge-charge, charge-spin, and spin-spin correlations. The non-magnetic state of the one-dimensional, half-filled Hubbard model is studied. Within the Gutzwiller approximation, the expression for the ground state energy can be worked out analytically. The correlation between empty and doubly occupied sites is found to play the most essential role. Minimization in the large-U limit shows that the Brinkman-Rice transition has been pushed to U → ∞, and the leading term of the ground state energy density is of order −t2/ U . In contrast to results obtained with the Gutzwiller wave function, we find that the band occupation number nk is monotonically decreasing both above and below kF. The dominant k–dependence is given by ~(t/U) cos k, in agreement with t/U–expansion results. nk has also a weak step-function component, with the discontinuity at kF vanishing as (t/U)2 in the limit U/t ≫ 1.

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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