Analytic wave functions and energies for two-dimensional $$ \mathcal{P}\mathcal{T} $$-symmetric quartic potentials

Open Physics ◽  
2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Vladimír Tichý ◽  
Lubomír Skála
Keyword(s):  
Wave Functions ◽  
Two Dimensional ◽  
Analytic Wave

AbstractAnalytic wave functions and the corresponding energies for a class of the $$ \mathcal{P}\mathcal{T} $$-symmetric two-dimensional quartic potentials are found. The general form of the solutions is discussed.

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.

Analytic Wave Functions. I. Atoms with1s,2s, and2pElectrons

1958 ◽  
Vol 111 (4) ◽  
pp. 1111-1113 ◽  
Author(s):  
R. G. Breene
Keyword(s):  
Wave Functions ◽  
Analytic Wave

Analytic Wave Functions. IV. Inclusion of Correlation

1962 ◽  
Vol 128 (5) ◽  
pp. 2190-2194
Author(s):  
R. G. Breene
Keyword(s):  
Wave Functions ◽  
Analytic Wave

scholarly journals BLACK HOLE UNCERTAINTIES

1993 ◽  
Vol 08 (20) ◽  
pp. 1925-1941
Author(s):  
ULF H. DANIELSSON
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Quantum Theory ◽  
Uncertainty Relation ◽  
Wave Functions ◽  
Uncertainty Relations ◽  
Two Dimensional ◽  
Black Hole Mass ◽  
Dilaton Black Holes

In this work the quantum theory of two-dimensional dilaton black holes is studied using the Wheeler-De Witt equation. The solutions correspond to wave functions of the black hole. It is found that for an observer inside the horizon, there are uncertainty relations for the black hole mass and a parameter in the metric determining the Hawking flux. Only for a particular value of this parameter can both be known with arbitrary accuracy. In the generic case there is instead a relation that is very similar to the so-called string uncertainty relation.

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