Two-dimensional Coulomb scattering of a quantum particle: Construction of radial wave functions

2016 ◽  
Vol 186 (1) ◽  
pp. 101-117 ◽  
Author(s):  
V. V. Pupyshev
Keyword(s):  
Quantum Particle ◽  
Wave Functions ◽  
Coulomb Scattering ◽  
Two Dimensional ◽  
Radial Wave

scholarly journals Visualizing the multifractal wave functions of a disordered two-dimensional electron gas

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Berthold Jäck ◽  
Fabian Zinser ◽  
Elio J. König ◽  
Sune N. P. Wissing ◽  
Anke B. Schmidt ◽  
...  
Keyword(s):  
Electron Gas ◽  
Wave Functions ◽  
Two Dimensional ◽  
Dimensional Electron ◽  
Two Dimensional Electron Gas ◽  
Dimensional Electron Gas

scholarly journals Reducing a Class of Two-Dimensional Integrals to One-Dimension with an Application to Gaussian Transforms

Atoms ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 53
Author(s):  
Jack C. Straton
Keyword(s):  
Quantum Theory ◽  
Arbitrary Function ◽  
Plane Waves ◽  
Wave Functions ◽  
One Dimension ◽  
Two Dimensional ◽  
Transition Amplitudes ◽  
Multidimensional Integrals ◽  
Coulomb Potentials

Quantum theory is awash in multidimensional integrals that contain exponentials in the integration variables, their inverses, and inverse polynomials of those variables. The present paper introduces a means to reduce pairs of such integrals to one dimension when the integrand contains powers multiplied by an arbitrary function of xy/(x+y) multiplying various combinations of exponentials. In some cases these exponentials arise directly from transition-amplitudes involving products of plane waves, hydrogenic wave functions, and Yukawa and/or Coulomb potentials. In other cases these exponentials arise from Gaussian transforms of such functions.

scholarly journals SPIN – A Schrödinger-Poisson Solver Including Nonparabolic Bands

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 489-493
Author(s):  
H. Kosina ◽  
C. Troger
Keyword(s):  
Dispersion Relation ◽  
Effective Mass ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Two Dimensional ◽  
Electron Systems ◽  
Dimensional Electron ◽  
One Dimensional ◽  
Poisson Solver ◽  
Two Dimensional Electron Systems

Nonparabolicity effects in two-dimensional electron systems are quantitatively analyzed. A formalism has been developed which allows to incorporate a nonparabolic bulk dispersion relation into the Schrödinger equation. As a consequence of nonparabolicity the wave functions depend on the in-plane momentum. Each subband is parametrized by its energy, effective mass and a subband nonparabolicity coefficient. The formalism is implemented in a one-dimensional Schrödinger-Poisson solver which is applicable both to silicon inversion layers and heterostructures.

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