Variational Method for the Ground State of LiquidHe4

1966 ◽  
Vol 17 (8) ◽  
pp. 424-426 ◽  
Author(s):  
Joon Chang Lee ◽  
A. A. Broyles
Keyword(s):  
Variational Method ◽  
Ground State

BUILT-IN ELECTRIC FIELD EFFECT ON DONOR IMPURITIES IN STRAINED WURTZITE GaN/AlGaN ASYMMETRIC DOUBLE QUANTUM WELLS

2012 ◽  
Vol 26 (26) ◽  
pp. 1250172 ◽  
Author(s):  
JUN ZHU ◽  
SHI LIANG BAN ◽  
SI HUA HA
Keyword(s):  
Variational Method ◽  
Electric Field ◽  
Quantum Wells ◽  
Ground State ◽  
Field Effect ◽  
Binding Energies ◽  
Double Quantum ◽  
Electric Field Effect ◽  
Material Parameters ◽  
Asymmetric Double Quantum Wells

The ground state binding energies of donor impurities in strained [0001]-oriented wurtzite GaN / Al x Ga 1-x N asymmetric double quantum wells are investigated using a variational method combined with numerical computation. The built-in electric field due to the spontaneous and strain-induced piezoelectric polarization and the strain modification on material parameters are taken into account. The variations of binding energies versus the width of central barrier, the ratio of two well widths, and the impurity position are presented, respectively. It is found that the built-in electric field causes a mutation of binding energies with increasing the width of central barrier to some value. The results for symmetrical double quantum wells and without the built-in electric field are also discussed for comparison.

Electronic wave functions II. A calculation for the ground state of the beryllium atom

1950 ◽  
Vol 201 (1064) ◽  
pp. 125-137 ◽  
Keyword(s):  
Wave Function ◽  
Variational Method ◽  
Ground State ◽  
Accurate Result ◽  
Energy Criterion ◽  
Wave Functions ◽  
Exponential Functions ◽  
Approximate Wave Function ◽  
Electronic Wave Functions ◽  
Approximate Wave

An approximate wave function expressed in terms of exponential functions, spherical harmonics, etc., with numerical coefficients has been calculated for the ground state of the beryllium atom . Judged by the energy criterion this gives a more accurate result than the Hartree result which was the best previously known. This has been calculated as a trial of a fresh method of calculating atomic wave functions. A linear combination of Slater determinants is treated by the variational method. The results suggest that this will provide a more powerful and convenient method than has previously been available for atoms with more than two electrons.

Variational Method for the Ground State of Multispecies Quantum Fluids

1968 ◽  
Vol 170 (1) ◽  
pp. 293-305 ◽  
Author(s):  
K. R. Allen ◽  
Tucson Dunn
Keyword(s):  
Variational Method ◽  
Ground State ◽  
Quantum Fluids

Variational study on the ground state of the spin XY magnet

1978 ◽  
Vol 56 (7) ◽  
pp. 902-912 ◽  
Author(s):  
Masuo Suzuki ◽  
Seiji Miyashita
Keyword(s):  
Wave Function ◽  
Variational Method ◽  
Ground State ◽  
State Energy ◽  
Finite Lattice ◽  
Long Range Order ◽  
Lattice Method ◽  
Approximate Wave Function ◽  
Approximate Wave ◽  
Variational Study

An approximate wave function of the ground state of the spin [Formula: see text] XY magnet is derived using a variational method. This wave function yields estimates of the ground state energy and long-range order which agree very well with the results obtained by Betts and Oitmaa by a finite lattice method.

scholarly journals Extended duality methods for nonlinear Helmholtz equations

2021 ◽  
Author(s):  
◽  
Tolga Yesil
Keyword(s):  
Variational Method ◽  
Helmholtz Equation ◽  
Ground State ◽  
Critical Case ◽  
Dual Method ◽  
Helmholtz Equations ◽  
Ground State Solutions ◽  
Duality Methods ◽  
Dual Variational Method ◽  
Nonlinear Helmholtz Equations

We provide extensions of the dual variational method for the nonlinear Helmholtz equation from Evéquoz and Weth. In particular we prove the existence of dual ground state solutions in the Sobolev critical case, extend the dual method beyond the standard Stein Tomas and Kenig Ruiz Sogge range and generalize the method for sign changing nonlinearities.

scholarly journals Positive ground state solutions for asymptotically periodic generalized quasilinear Schrödinger equations

2021 ◽  
Vol 7 (1) ◽  
pp. 1015-1034
Author(s):  
Shulin Zhang ◽  
◽  
Keyword(s):  
Variational Method ◽  
Ground State ◽  
Periodic Potential ◽  
Ground State Solution ◽  
State Solution ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Ground State Solutions ◽  
Asymptotically Periodic

<abstract><p>In this paper, we study the existence of a positive ground state solution for a class of generalized quasilinear Schrödinger equations with asymptotically periodic potential. By the variational method, a positive ground state solution is obtained. Compared with the existing results, our results improve and generalize some existing related results.</p></abstract>

Variational method for excited states from supersymmetric techniques

2003 ◽  
Vol 81 (11) ◽  
pp. 1283-1291 ◽  
Author(s):  
G RP Borges ◽  
A de Souza Dutra ◽  
Elso Drigo ◽  
J R Ruggiero
Keyword(s):  
Variational Method ◽  
Numerical Integration ◽  
Excited States ◽  
Ground State ◽  
Potential Parameter ◽  
The One ◽  
Double Well Potential ◽  
Good Agreement ◽  
03.65 Ge

We suggest a method for constructing trial eigenfunctions for excited states to be used in the variational method. This method is a generalization of the one that uses a superpotential to obtain the trial functions for the ground state. The construction of an effective hierarchy of Hamiltonians is used to determine excited variational energies. The first four eigenvalues for a quartic double-well potential are calculated for several values of the potential parameter. The results are in very good agreement with the eigenvalues obtained by numerical integration. PACS Nos.: 11.30.Pb, 03.65.Ge

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