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.

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.

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 Inferring Single-Cell 3D Chromosomal Structures Based on the Lennard-Jones Potential

2021 ◽  
Vol 22 (11) ◽  
pp. 5914
Author(s):  
Mengsheng Zha ◽  
Nan Wang ◽  
Chaoyang Zhang ◽  
Zheng Wang
Keyword(s):  
Single Cell ◽  
Loss Function ◽  
Gaussian Function ◽  
Three Dimensional ◽  
Lennard Jones Potential ◽  
Jones Potential ◽  
Cubic Lattice ◽  
Lennard Jones ◽  
3D Fish ◽  
Well Depth

Reconstructing three-dimensional (3D) chromosomal structures based on single-cell Hi-C data is a challenging scientific problem due to the extreme sparseness of the single-cell Hi-C data. In this research, we used the Lennard-Jones potential to reconstruct both 500 kb and high-resolution 50 kb chromosomal structures based on single-cell Hi-C data. A chromosome was represented by a string of 500 kb or 50 kb DNA beads and put into a 3D cubic lattice for simulations. A 2D Gaussian function was used to impute the sparse single-cell Hi-C contact matrices. We designed a novel loss function based on the Lennard-Jones potential, in which the ε value, i.e., the well depth, was used to indicate how stable the binding of every pair of beads is. For the bead pairs that have single-cell Hi-C contacts and their neighboring bead pairs, the loss function assigns them stronger binding stability. The Metropolis–Hastings algorithm was used to try different locations for the DNA beads, and simulated annealing was used to optimize the loss function. We proved the correctness and validness of the reconstructed 3D structures by evaluating the models according to multiple criteria and comparing the models with 3D-FISH data.

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