REPRESENTATIONS OF THE UNITARY GROUP AND WAVE FUNCTIONS

1961 ◽  
Vol 39 (4) ◽  
pp. 510-513
Author(s):  
H. A. Venables
Keyword(s):  
Spherical Harmonics ◽  
Unitary Group ◽  
Wave Functions ◽  
Irreducible Representations ◽  
Two Dimensional

A number of wave functions besides the spherical harmonics are obtainable from the irreducible representations of the two-dimensional unitary group.

An algebraic criterion for symmetric Hopf bifurcation

1993 ◽  
Vol 440 (1910) ◽  
pp. 727-732 ◽  
Keyword(s):  
Fixed Point ◽  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Spherical Harmonics ◽  
Irreducible Representations ◽  
Two Dimensional ◽  
Bifurcation Theorem ◽  
Algebraic Criterion ◽  
Equivariant Hopf Bifurcation

The equivariant Hopf bifurcation theorem states that bifurcating branches of periodic solutions with certain symmetries exist when the fixed-point subspace of that subgroup of symmetries is two dimensional. We show that there is a group-theoretic restriction on the subgroup of symmetries in order for that subgroup to have a two-dimensional fixed-point subspace in any representation. We illustrate this technique for all irreducible representations of SO(3) on the space V l of spherical harmonics for l even.

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.

On particle-like representations of the complete homogeneous Lorentz group

1973 ◽  
Vol 74 (1) ◽  
pp. 149-160 ◽  
Author(s):  
J. A. de Wet
Keyword(s):  
Lorentz Group ◽  
Wave Functions ◽  
Unitary Groups ◽  
Irreducible Representations ◽  
Electron Wave ◽  
Precise Form ◽  
Homogeneous Lorentz Group ◽  
The Many ◽  
Matrix Contraction

In two previous papers (1, 2) representations of the unitary groups U4, U2 were found which described some of the properties of nucleons and electrons. In particular, the many electron wave functions were constructed from the irreducible representations of U2 restricted to the proper orthochronous Lorentz group Lp. In this paper the irreducible representations of U4 found in (1) will be shown to be also irreducible representations of the complete homogeneous Lorentz group L0 and the techniques of matrix contraction employed in (2) will be used to find the precise form of the matrices of the infinitesimal ring.

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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