New Method to Construct Parabolic Coordinates

Abstract

Victor G. Zakharov

In this paper, we consider fully original method to construct the orthogonal parabolic coordinates [1],[2] for any dimension N. Unlike the three-dimensional case that is produced by rotation about the parabolic symmetry axis, we join three paraboloids that possess three-fold rotational symmetry. In N-dimensional case, we combine N paraboloids that have rotational symmetry of order N. Moreover, for any dimension, we can obtain the Laplace-Runge-Lenz vector.

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