SUPERSYMMETRY, VARIATIONAL METHOD AND THE LENNARD–JONES (12,6) POTENTIAL

2001 ◽  
Vol 16 (27) ◽  
pp. 4401-4407 ◽  
Author(s):  
GLÁUCIA ROSÂNGELA PEGLOW BORGES ◽  
ELSO DRIGO FILHO
Keyword(s):  
Quantum Mechanics ◽  
Variational Method ◽  
Effective Potential ◽  
Supersymmetric Quantum Mechanics ◽  
Lennard Jones

The formalism of supersymmetric quantum mechanics is used to determine trial functions in order to obtain eigenvalues for the Lennard–Jones (12,6) potential from variational method. The superpotential obtained provides an effective potential which can be directly comparable to the original one.

CONFINED LENNARD–JONES POTENTIAL: A VARIATIONAL TREATMENT

2010 ◽  
Vol 25 (08) ◽  
pp. 641-648 ◽  
Author(s):  
F. R. SILVA ◽  
E. DRIGO FILHO
Keyword(s):  
Quantum Mechanics ◽  
Variational Method ◽  
Energy Levels ◽  
Numerical Results ◽  
Supersymmetric Quantum Mechanics ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Energy Eigenvalues ◽  
Lennard Jones ◽  
Variational Treatment

In this work, the energy eigenvalues for the confined Lennard–Jones potential are calculated through the Variational Method allied to the Supersymmetric Quantum Mechanics. Numerical results are obtained for different energy levels, parameters of the potential and values of confinement radius. In the limit, where this radius assumes great values, the results for the non-confined case are recovered.

IMPROVED SUSY INSPIRED VARIATIONAL METHOD TO OBTAIN BOUND STATE ENERGIES OF THE SCREENED COULOMB POTENTIAL

2003 ◽  
Vol 18 (12) ◽  
pp. 853-857
Author(s):  
SUBIR K. BOSE ◽  
AXEL SCHULZE-HALBERG
Keyword(s):  
Quantum Mechanics ◽  
Variational Method ◽  
Coulomb Potential ◽  
Trial Function ◽  
Bound State ◽  
Supersymmetric Quantum Mechanics ◽  
Screened Coulomb Potential

We improve a result obtained in Ref. 2: In the context of supersymmetric quantum mechanics we present a certain superpotential that yields a trial function we use for the calculation of variational quantum bound state energies of the screened Coulomb potential. We show that for small screening parameters our trial function yields better approximations for the energies than the trial function used in Ref. 2.

scholarly journals INDUCED VARIATIONAL METHOD FROM SUPERSYMMETRIC QUANTUM MECHANICS AND THE SCREENED COULOMB POTENTIAL

2000 ◽  
Vol 15 (19) ◽  
pp. 1253-1259 ◽  
Author(s):  
ELSO DRIGO FILHO ◽  
REGINA MARIA RICOTTA
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Variational Method ◽  
Coulomb Potential ◽  
Trial Wave Function ◽  
Supersymmetric Quantum Mechanics ◽  
Exact Results ◽  
Energy Eigenvalues ◽  
Screened Coulomb Potential

The formalism of supersymmetric quantum mechanics supplies a trial wave function to be used in the variational method. The screened Coulomb potential is analyzed within this approach. Numerical and exact results for energy eigenvalues are compared.

scholarly journals SUPERSYMMETRY, VARIATIONAL METHOD AND HULTHÉN POTENTIAL

1995 ◽  
Vol 10 (22) ◽  
pp. 1613-1618 ◽  
Author(s):  
ELSO DRIGO FILHO ◽  
REGINA MARIA RICOTTA
Keyword(s):  
Quantum Mechanics ◽  
Variational Method ◽  
Supersymmetric Quantum Mechanics ◽  
Hulthén Potential ◽  
Hulthen Potential

The formalism of supersymmetric quantum mechanics provides us with the eigenfunctions to be used in the variational method to obtain the eigenvalues for the Hulthén potential.

scholarly journals ABCD of ’t Hooft operators

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hirotaka Hayashi ◽  
Takuya Okuda ◽  
Yutaka Yoshida
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theories ◽  
Supersymmetric Quantum Mechanics ◽  
Type Ii ◽  
Expectation Values ◽  
String Theories

Abstract We compute by supersymmetric localization the expectation values of half-BPS ’t Hooft line operators in $$ \mathcal{N} $$ N = 2 U(N ), SO(N ) and USp(N ) gauge theories on S1 × ℝ3 with an Ω-deformation. We evaluate the non-perturbative contributions due to monopole screening by calculating the supersymmetric indices of the corresponding supersymmetric quantum mechanics, which we obtain by realizing the gauge theories and the ’t Hooft operators using branes and orientifolds in type II string theories.

scholarly journals Local G2-manifolds, Higgs bundles and a colored quantum mechanics

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Max Hübner
Keyword(s):  
Quantum Mechanics ◽  
Gauge Theories ◽  
Supersymmetric Quantum Mechanics ◽  
Higgs Bundle ◽  
Higgs Bundles ◽  
View Point ◽  
Yang Mills ◽  
G2 Manifolds ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract M-theory on local G2-manifolds engineers 4d minimally supersymmetric gauge theories. We consider ALE-fibered G2-manifolds and study the 4d physics from the view point of a partially twisted 7d supersymmetric Yang-Mills theory and its Higgs bundle. Euclidean M2-brane instantons descend to non-perturbative effects of the 7d supersymmetric Yang-Mills theory, which are found to be in one to one correspondence with the instantons of a colored supersymmetric quantum mechanics. We compute the contributions of M2-brane instantons to the 4d superpotential in the effective 7d description via localization in the colored quantum mechanics. Further we consider non-split Higgs bundles and analyze their 4d spectrum.

scholarly journals Wronskian differential formula for confluent supersymmetric quantum mechanics

2012 ◽  
Vol 376 (5) ◽  
pp. 692-696 ◽  
Author(s):  
David Bermudez ◽  
David J. Fernández C. ◽  
Nicolás Fernández-García
Keyword(s):  
Quantum Mechanics ◽  
Supersymmetric Quantum Mechanics
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