Representation of the Green's function of Schrödinger's equation with almost periodic potential by a path integral over coherent states

2006 ◽  
Vol 197 (11) ◽  
pp. 1559-1568
Author(s):  
A A Arsen'ev
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Path Integral ◽  
Coherent States ◽  
Periodic Potential ◽  
Almost Periodic ◽  
Schrödinger’S Equation ◽  
Schrödinger's Equation

PATH INTEGRAL CALCULATION OF GREEN’S FUNCTION FOR SCHRÖDINGER EQUATION IN UNITARY GAUGE

1992 ◽  
Vol 07 (31) ◽  
pp. 7775-7786
Author(s):  
L. ROZANSKY
Keyword(s):  
Schrödinger Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Path Integral ◽  
Schrodinger Equation ◽  
Preexponential Factor ◽  
Unitary Gauge ◽  
Gauge Fixing

Green’s function of Schrödinger equation is represented as a time-reparametrization invariant path integral. Unitary gauge fixing enables us to get the WKB preexponential factor without calculating determinants of operators containing derivatives.

scholarly journals Green’s Function for Dirac Particle in a Non-Abelian Field: A Path Integral Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Sami Boudieb ◽  
Lyazid Chetouani
Keyword(s):  
Green Function ◽  
Green’S Function ◽  
Green's Function ◽  
Path Integral ◽  
Dirac Particle ◽  
Integral Approach ◽  
Path Integral Approach ◽  
Abelian Field ◽  
The Green Function

The Green function for a Dirac particle moving in a non-Abelian field and having a particular form is exactly determined by the path integral approach. The wave functions were deduced from the residues of Green’s function. It is shown that the classical paths contributed mainly to the determination of the Green function.

Analysis of Bloch’s Method in Structures with Energy Dissipation

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Farhad Farzbod ◽  
Michael J. Leamy
Keyword(s):  
Energy Dissipation ◽  
Periodic Potential ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Periodic Systems ◽  
Crystalline Solid ◽  
Structural Damping ◽  
Electron Wave ◽  
Schrödinger’S Equation ◽  
Schrödinger's Equation

Bloch analysis was originally developed to solve Schrödinger’s equation for the electron wave function in a periodic potential field, such as found in a pristine crystalline solid. In the context of Schrödinger’s equation, damping is absent and energy is conserved. More recently, Bloch analysis has found application in periodic macroscale materials, such as photonic and phononic crystals. In the vibration analysis of phononic crystals, structural damping is present together with energy dissipation. As a result, application of Bloch analysis is not straightforward and requires additional considerations in order to obtain valid results. It is the intent of this paper to propose a general framework for applying Bloch analysis in such systems. Results are presented in which the approach is applied to example phononic crystals. These results reveal the manner in which damping affects dispersion and the presence of band gaps in periodic systems.

scholarly journals REGULARIZED GREEN'S FUNCTION FOR THE INVERSE SQUARE POTENTIAL

2002 ◽  
Vol 17 (13) ◽  
pp. 817-826 ◽  
Author(s):  
HORACIO E. CAMBLONG ◽  
CARLOS R. ORDÓÑEZ
Keyword(s):  
Quantum Mechanics ◽  
Green’S Function ◽  
Green's Function ◽  
Path Integral ◽  
Real Space ◽  
Liouville Theory ◽  
Hyperspherical Coordinates ◽  
Closed Expression ◽  
Integral Treatment ◽  
Sturm Liouville

A Green's function approach is presented for the D-dimensional inverse square potential in quantum mechanics. This approach is implemented by the introduction of hyperspherical coordinates and the use of a real-space regulator in the regularized version of the model. The application of Sturm–Liouville theory yields a closed expression for the radial energy Green's function. Finally, the equivalence with a recent path-integral treatment of the same problem is explicitly shown.

Dirac particle in Aharonov–Bohm–Coulomb field: Path integral treatment

2022 ◽  
Author(s):  
A. Merdaci ◽  
N. Boudiaf ◽  
L. Chetouani
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Path Integral ◽  
Spin Dynamics ◽  
Coulomb Field ◽  
Dirac Particle ◽  
Coordinate Space ◽  
Relativistic Limit ◽  
Integral Treatment ◽  
Aharonov Bohm

Exact Green’s function related to a Dirac particle submitted to the combination of Aharonov–Bohm and Coulomb potentials in [Formula: see text]) coordinate space is analytically calculated via path integral formalism. The Pauli matrices which describe the spin dynamics are replaced by two fermionic oscillators via the Schwinger model. The energy spectrum as well as the corresponding normalized wave functions are extracted following this approach. The interesting properties of the spinors are thus deduced after symmetrization. According to the symmetric form for Green’s function, it is shown that the non-relativistic limit of the Dirac particle is undertaken with much ease.

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