Open AccessJournal Article
The hydrogen atom via the four-dimensional spherical harmonics
TLDR
In this article, it was shown that the four-dimensional spherical harmonics separable in Euler angles correspond to solutions of the time-independent Schrodinger equation that are separability in parabolic coordinates.Abstract:
Using the fact that the Schrodinger equation for the stationary states of the hydrogen atom is equivalent to an integral equation on the unit sphere in a four-dimensional space, the eigenvalues, the eigenfunctions, and a dynamical symmetry group for this problem are obtained from the four-dimensional spherical harmonics and the group of rotations on the sphere. It is shown that the four-dimensional spherical harmonics separable in Euler angles correspond to solutions of the time-independent Schrodinger equation that are separable in parabolic coordinatesread more
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Patent
Method and system
TL;DR: In this paper, a method and system for modelling atomic or molecular level structures or the atomic energies or forces in such structures is described, which use a Gaussian Process to estimate properties at the atom or molecular levels in these structures.
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A generating function for the spherical harmonics in p dimensions
TL;DR: In this paper, a generating function for the spherical harmonics in three or more dimensions is given, which allows us to find in a simple manner the explicit expressions for spherical harmonic in three dimensions.
Journal ArticleDOI
Green function of the Poisson equation: D = 2, 3, 4
TL;DR: In this article, the authors study the Poisson equation in two, three and four dimensions, where the solution g of the equation, where and are D-dimensional position vectors, is customarily expanded into radial and angular coordinates.
Patent
Method and system for estimating properties of atoms and molecules
TL;DR: In this article, a Gaussian Process is used to estimate properties at the atom or molecular level in such structures, or the atomic or molecular energies or forces in these structures, respectively.
References
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Book
Mathematical Methods for Physicists
TL;DR: In this article, the authors present a model for vector analysis based on the Calculus of Variations and the Sturm-Liouville theory, which includes the following: Curved Coordinates, Tensors.