Computation of the ground state energy of the Schrödinger equation by a Monte Carlo method

2021 ◽  
Vol 49 (1) ◽  
Author(s):  
Adam Puchalski
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Schrödinger Equation ◽  
Ground State Energy ◽  
Ground State ◽  
Schrodinger Equation ◽  
State Energy

Degenerate trajectories and Hamiltonian envelopes in the method of self-similar approximations

1993 ◽  
Vol 71 (11-12) ◽  
pp. 537-546 ◽  
Author(s):  
V. I. Yukalov ◽  
E. P. Yukalova
Keyword(s):  
Schrödinger Equation ◽  
Ground State Energy ◽  
Ground State ◽  
Schrodinger Equation ◽  
Approximate Calculation ◽  
State Energy ◽  
Anharmonic Oscillator ◽  
New Techniques ◽  
Self Similar ◽  
Very High

We study two new techniques for the approximate calculation of the eigenvalues of the Schrödinger equation. These techniques are variants of the method of self-similar approximations suggested recently by one of the authors. We illustrate the ideas by an anharmonic oscillator problem. We show that the precision of the method can be very high. For example, the ground-state energy of an anharmonic oscillator can be calculated with an error not exceeding 0.07% for all anharmonicity parameters ranging from zero to infinity.

GROUND-STATE PROPERTIES OF THE SPIN-1/2 ANTIFERROMAGNETIC HEISENBERG MODEL ON A CUBIC LATTICE BY A MONTE CARLO METHOD

1995 ◽  
Vol 09 (10) ◽  
pp. 619-627 ◽  
Author(s):  
R. A. SAUERWEIN ◽  
M. J. DE OLIVEIRA
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Ground State Energy ◽  
Ground State ◽  
Heisenberg Model ◽  
State Energy ◽  
Isotropic Case ◽  
Spatial Anisotropy ◽  
Cubic Lattice ◽  
Antiferromagnetic Heisenberg Model

The spin-1/2 antiferromagnetic Heisenberg model with spatial anisotropy is studied on a cubic lattice by a Monte Carlo Method. Two types of spatial anisotropies are considered: planar and axial. The staggered magnetization m† and the ground state energy per site ∊0 are obtained as a function of the anisotropy. In the isotropic case we have obtained m† = 0.429 ± 0.001 in units where the saturated value is 0.5 and ∊0 = –0.899 ± 0.001.

AN IMPROVED RESULT ON GROUND STATE SOLUTIONS OF QUASILINEAR SCHRÖDINGER EQUATIONS WITH SUPER-LINEAR NONLINEARITIES

2018 ◽  
Vol 99 (2) ◽  
pp. 231-241
Author(s):  
SITONG CHEN ◽  
ZU GAO
Keyword(s):  
Schrödinger Equation ◽  
Ground State Energy ◽  
Ground State ◽  
Schrodinger Equation ◽  
State Energy ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Quasilinear Schrödinger Equation ◽  
Ground State Solutions

By using variational and some new analytic techniques, we prove the existence of ground state solutions for the quasilinear Schrödinger equation with variable potentials and super-linear nonlinearities. Moreover, we establish a minimax characterisation of the ground state energy. Our result improves and extends the existing results in the literature.

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.

scholarly journals About calculation of the ground-state energy of the helium atom

2021 ◽  
Vol 2067 (1) ◽  
pp. 012002
Author(s):  
E V Baklanov ◽  
P V Pokasov ◽  
A V Taichenachev
Keyword(s):  
Perturbation Theory ◽  
Numerical Calculation ◽  
Schrödinger Equation ◽  
Helium Atom ◽  
Ground State Energy ◽  
Ground State ◽  
Schrodinger Equation ◽  
State Energy ◽  
Calculation Results ◽  
The Difference

Abstract Two versions of the numerical calculation of the ground state energy of the helium atom are compared. First, the nonrelativistic Schrödinger equation with a fixed nucleus is solved, and then the perturbation theory is used. Another version solves this problem exactly. Comparison shows that the difference between the calculation results is 94 kHz.

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