Dirac Hamiltonian with Coulomb Potential and Contact Interaction on a Sphere

1990 ◽  
pp. 209-219
Author(s):  
J. Dittrich ◽  
P. Exner ◽  
P. Šeba
Keyword(s):  
Contact Interaction ◽  
Coulomb Potential ◽  
Dirac Hamiltonian

Dirac Hamiltonian with Coulomb potential and spherically symmetric shell contact interactiona)

1992 ◽  
Vol 33 (6) ◽  
pp. 2207-2214 ◽  
Author(s):  
J. Dittrich ◽  
P. Exner ◽  
P. Šeba
Keyword(s):  
Coulomb Potential ◽  
Spherically Symmetric ◽  
Dirac Hamiltonian

scholarly journals AN "ACCIDENTAL" SYMMETRY OPERATOR FOR THE DIRAC EQUATION IN THE COULOMB POTENTIAL

2005 ◽  
Vol 20 (30) ◽  
pp. 2277-2281 ◽  
Author(s):  
TAMARI T. KHACHIDZE ◽  
ANZOR A. KHELASHVILI
Keyword(s):  
Dirac Equation ◽  
Linear Combination ◽  
Coulomb Potential ◽  
Coulomb Field ◽  
Symmetry Operator ◽  
Dirac Hamiltonian ◽  
Accidental Symmetry

On the basis of the generalization of the theorem about K-odd operators (K is the Dirac's operator), certain linear combination is constructed, which appears to commute with the Dirac Hamiltonian for Coulomb field. This operator coincides with the Johnson and Lippmann operator and is closely connected to the familiar Laplace–Runge–Lenz vector. Our approach guarantees not only derivation of Johnson–Lippmann operator, but simultaneously commutativity with the Dirac Hamiltonian.

INVESTIGATION OF DEPENDENCE IMPACT OF TOOL GEOMETRICAL PARAMETERS AND CUTTING SPEED UPON SHAPING EFFORT AT HELICAL GROOVE CUTTING ON INTERNAL SURFACE OF CYLINDRICAL SHELL

2020 ◽  
Vol 2020 (10) ◽  
pp. 22-28
Author(s):  
Vadim Kuc ◽  
Dmitriy Gridin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cylindrical Shell ◽  
Contact Interaction ◽  
Cutting Speed ◽  
Internal Surface ◽  
Geometrical Parameters ◽  
Software Complex ◽  
Helical Groove ◽  
Groove Cutting

The work purpose was the investigation of dependence impact of tool geometrical parameters upon shaping effort during internal groove cutting. As a realization for the fulfillment of the helical groove processing investigation there was used a software complex based on a finite element method and a computer mathematic system. As a result of the investigations carried out there was obtained a regression equation manifesting the dependence of factors impact upon axial force falling on one tooth of the tool in the set scale of factor parameters. The scientific novelty consists in that in the paper there is considered a new method for helical groove cutting in which a shaping motion is carried out at the expense of the contact interaction of a tool and a billet performing free cutting. The investigation results obtained allowed determining the number of teeth operating simultaneously, that can be used further at cutting mode setting, and also as recommendations during designing tool design.

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

Improving the service life of coatings during running-in

2019 ◽  
pp. 58-64
Author(s):  
I. R. Aslanyan
Keyword(s):  
Mathematical Modeling ◽  
Service Life ◽  
Contact Interaction ◽  
Phosphate Coatings ◽  
The Way

In work researches of phosphate coatings are conducted. By means of methods of mathematical modeling of contact interaction it is established that on wear of phosphate coatings the greatest influence renders their roughness. For decrease in wear of the running-in coverings applied to protection of steel products, the way on increase in service life of phosphate coatings is offered.

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