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Two‐dimensional hydrogen atom confined in circles, angles, and circular sectors
Author(s) -
ChaosCador L.,
LeyKoo E.
Publication year - 2005
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.20540
Subject(s) - hydrogen atom , polarizability , eigenfunction , dipole , eigenvalues and eigenvectors , atom (system on chip) , atomic physics , parabolic coordinates , moment (physics) , physics , quantum number , separable space , chemistry , quantum mechanics , mathematics , mathematical analysis , molecule , log polar coordinates , orthogonal coordinates , group (periodic table) , embedded system , computer science
The Schrödinger equation for the 2D hydrogen atom is separable in circular coordinates (ρ = $\sqrt{x^{2} + y^{2}}$ , φ = tan −1 y / x ). In this article the energy eigenvalues and eigenfunctions of such an atom in three different situations of confinement inside (a) a circle (0 ≤ ρ ≤ ρ 0 , 0 ≤ φ ≤ 2π), (b) an angle (0 ≤ ρ ≤ ∞, 0 ≤ φ ≤ φ 0 ), and (c) a circular sector (0 ≤ ρ ≤ ρ 0 , 0 ≤ φ ≤ φ 0 ) are explicitly constructed. Characteristic properties of the atom in its ground state for each situation of confinement such as the polarizability for (a) and electric dipole moment for (b) and (c) are also evaluated. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005