We consider the action of the quadratic form of the Laplace operator and its extensions in subspaces of linear combinations of the “transverse” and “longitudinal” functions with the fixed orbital momentum with respect to the coordinate origin. In the statement of the problem, it is required that the extensions obtained, after the transfer back to the space of vector functions, can be represented as simple limit expressions with two coefficients. We study the behavior of these coefficients with respect to the initial choice of the linear subspace. Bibliography: 5 titles.
Similar content being viewed by others
References
F. A. Berezin and L. D. Faddeev, “A remark on Schrödinger’s equation with a singular potential,” Dokl. Akad. Nauk, Ser. Fiz., 137, 1011 (1961).
T. A. Bolokhov, “Quantum Hamiltonian eigenstates for a free transverse field,” arxiv:1512.04121.
E. L. Hill, “The theory of vector spherical harmonics,” Amer. J. Phys., 22, 211 (1954).
T. A. Bolokhov, “Extensions of the quadratic form of the transverse Laplace operator,” Zap. Nauchn. Semin. POMI, 213, 78–110 (2015).
T. A. Bolokhov, “Properties of the radial part of the Laplace operator for l = 1 in a special scalar product,” Zap. Nauchn. Semin. POMI, 434, 32–52 (2015).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by T. A. Bolokhov.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 447, 2016, pp. 5–19.
Rights and permissions
About this article
Cite this article
Bolokhov, T.A. Properties of Some Extensions of the Quadratic Form of the Vector Laplace Operator. J Math Sci 229, 487–496 (2018). https://doi.org/10.1007/s10958-018-3691-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-018-3691-6