scholarly journals Unfolding spinor wave functions and expectation values of general operators: Introducing the unfolding-density operator

2015 ◽  
Vol 91 (4) ◽  
Author(s):  
Paulo V. C. Medeiros ◽  
Stepan S. Tsirkin ◽  
Sven Stafström ◽  
Jonas Björk
Keyword(s):  
Density Operator ◽  
Wave Functions ◽  
Expectation Values ◽  
Spinor Wave

scholarly journals Quantum electrodynamics with self-conjugated equations with spinor wave functions for fermion fields

2021 ◽  
pp. 2150086
Author(s):  
V. P. Neznamov ◽  
V. E. Shemarulin
Keyword(s):  
Cross Sections ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Lamb Shift ◽  
Wave Functions ◽  
Self Energy ◽  
Fermion Fields ◽  
Spinor Wave

Quantum electrodynamics (QED) with self-conjugated equations with spinor wave functions for fermion fields is considered. In the low order of the perturbation theory, matrix elements of some of QED physical processes are calculated. The final results coincide with cross-sections calculated in the standard QED. The self-energy of an electron and amplitudes of processes associated with determination of the anomalous magnetic moment of an electron and Lamb shift are calculated. These results agree with the results in the standard QED. Distinctive feature of the developed theory is the fact that only states with positive energies are present in the intermediate virtual states in the calculations of the electron self-energy, anomalous magnetic moment of an electron and Lamb shift. Besides, in equations, masses of particles and antiparticles have the opposite signs.

TWO-ELECTRON SYSTEM IN THE FIELD OF GENERALIZED SCREENED POTENTIAL

2011 ◽  
Vol 25 (19) ◽  
pp. 1619-1629 ◽  
Author(s):  
ARIJIT GHOSHAL ◽  
Y. K. HO
Keyword(s):  
Wave Function ◽  
Ground State ◽  
Electron System ◽  
Wave Functions ◽  
Expectation Values ◽  
Screening Parameter ◽  
System Ground State ◽  
Highly Correlated ◽  
First Time ◽  
Ground State Energies

Ground states of a two-electron system in generalized screened potential (GSP) with screening parameter λ: [Formula: see text] where ∊ is a constant, have been investigated. Employing highly correlated and extensive wave functions in Ritz's variational principle, we have been able to determine accurate ground state energies and wave functions of a two-electron system for different values of the screening parameter λ and the constant ∊. Convergence of the ground state energies with the increase of the number of terms in the wave function are shown. We also report various geometrical expectation values associated with the system, ground state energies of the corresponding one-electron system and the ionization potentials of the system. Such a calculation for the ground state of a two-electron system in GSP is carried out for first time in the literature.

EXACT SOLUTIONS OF DIRAC EQUATION FOR A NEW SPHERICALLY ASYMMETRICAL SINGULAR OSCILLATOR

2010 ◽  
Vol 25 (33) ◽  
pp. 2849-2857 ◽  
Author(s):  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Vector Potential ◽  
State Energy ◽  
Energy Levels ◽  
Scalar Potential ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Exact Bound ◽  
Spinor Wave

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of scalar and vector spherically asymmetrical singular oscillators. This is done provided that the vector potential is equal to the scalar potential. The spinor wave functions and bound state energy levels are presented. The case V(r) = -S(r) is also considered.

scholarly journals SLATER DECOMPOSITION OF LAUGHLIN STATES

1993 ◽  
Vol 07 (28) ◽  
pp. 4783-4813 ◽  
Author(s):  
GERALD V. DUNNE
Keyword(s):  
Density Operator ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Expectation Values ◽  
Filling Fraction ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Laughlin States ◽  
Expansion Coefficients ◽  
Slater Basis

The second-quantized form of the Laughlin states for the fractional quantum Hall effect is discussed by decomposing the Laughlin wavefunctions into the N-particle Slater basis. A general formula is given for the expansion coefficients in terms of the characters of the symmetric group, and the expansion coefficients are shown to possess numerous interesting symmetries. For expectation values of the density operator it is possible to identify individual dominant Slater states of the correct uniform bulk density and filling fraction in the physically relevant N→∞ limit.

scholarly journals Pseudospin and Spin Symmetric Solutions of the Dirac Equation: Hellmann Potential,Wei–Hua Potential, Varshni Potential

2014 ◽  
Vol 69 (3-4) ◽  
pp. 163-172 ◽  
Author(s):  
Altuğ Arda ◽  
Ramazan Sever
Keyword(s):  
Dirac Equation ◽  
Analytical Solutions ◽  
Energy Eigenvalue ◽  
Wave Functions ◽  
K Value ◽  
Energy Eigenvalues ◽  
Approximate Analytical Solutions ◽  
Hellmann Potential ◽  
Uvarov Method ◽  
Spinor Wave

Approximate analytical solutions of the Dirac equation are obtained for the Hellmann potential, the Wei-Hua potential, and the Varshni potential with any k-value for the cases having the Dirac equation pseudospin and spin symmetries. Closed forms of the energy eigenvalue equations and the spinor wave functions are obtained by using the Nikiforov-Uvarov method and some tables are given to see the dependence of the energy eigenvalues on different quantum number pairs (n;κ).

DISCUSSION OF A KNOWN SPHERICAL BASIS FOR DIRAC WAVE FUNCTIONS

2013 ◽  
Vol 28 (08) ◽  
pp. 1350022
Author(s):  
WERNER SCHEID
Keyword(s):  
Boundary Condition ◽  
Dirac Equation ◽  
Bound States ◽  
Wave Functions ◽  
Expectation Values ◽  
Original Boundary ◽  
Mit Bag Model ◽  
Slight Extension ◽  
Spherical Basis ◽  
Coulomb Potentials

The paper considers the free spherical Dirac equation with a boundary condition at r = R which is a slight extension of the original boundary condition of the MIT bag model. We discuss the basis states and apply them for a diagonalization of Coulomb potentials. The obtained results agree quite well with the lowest bound states with κ = -1, +1 and -2 and their expectation values [Formula: see text]. There appear basis states with energies -mc2 < E < mc2 under certain circumstances of the boundary condition. These states are concentrated at the boundary.

scholarly journals Canonical formalism and quantization of a massless spinning bosonic particle in four dimensions

2014 ◽  
Vol 29 (08) ◽  
pp. 1450044 ◽  
Author(s):  
Shinichi Deguchi ◽  
Shouma Negishi ◽  
Satoshi Okano ◽  
Takafumi Suzuki
Keyword(s):  
Minkowski Space ◽  
Canonical Formalism ◽  
Wave Functions ◽  
Dimensional Parameter ◽  
Spinning Particle ◽  
Plane Wave Solution ◽  
Four Dimensions ◽  
Constrained Hamiltonian Systems ◽  
Dimensional Minkowski Space ◽  
Spinor Wave

A twistor model of a free massless spinning particle in four-dimensional Minkowski space is studied in terms of space–time and spinor variables. This model is specified by a simple action, referred to here as the gauged Shirafuji action, that consists of twistor variables and gauge fields on the one-dimensional parameter space. We consider the canonical formalism of the model by following the Dirac formulation for constrained Hamiltonian systems. In the subsequent quantization procedure, we obtain a plane-wave solution with momentum spinors. From this solution and coefficient functions, we construct positive-frequency and negative-frequency spinor wave functions defined on complexified Minkowski space. It is shown that the Fourier–Laplace transforms of the coefficient functions lead to the spinor wave functions expressed as the Penrose transforms of the corresponding holomorphic functions on twistor space. We also consider the exponential generating function for the spinor wave functions and derive a novel representation for each of the spinor wave functions.

Energies, radial expectation values, hyperfine structures of the ground state and highly excited states for C and O2+

2020 ◽  
Vol 34 (20) ◽  
pp. 2050197
Author(s):  
Chao Chen
Keyword(s):  
Excited States ◽  
Ground State ◽  
Magnetic Coupling ◽  
Wave Functions ◽  
Coupling Constants ◽  
Future Research ◽  
Expectation Values ◽  
Radiative Transitions ◽  
Experimental Values ◽  
Hyperfine Structures

The Rayleigh–Ritz variational method with multiconfiguration interaction wave functions is used to calculate energies, radiative transitions and radial expectation values of the [Formula: see text] [Formula: see text] ground state and the [Formula: see text], [Formula: see text], [Formula: see text] highly excited states of C and [Formula: see text]. Hyperfine structure parameters and magnetic coupling constants of these states are also calculated in this work. The present calculations agree well with theoretical and experimental values available in the literature. Other data not reported in the literature are expected to offer valuable benchmarks for future research.

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