The hydrogen atom in a semi-infinite space with an elliptical cone boundary
| Autor: | R. Méndez-Fragoso, Eugenio Ley-Koo |
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| Rok vydání: | 2010 |
| Předmět: |
Physics
Angular momentum Hydrogen atom Eigenfunction Condensed Matter Physics Atomic and Molecular Physics and Optics Schrödinger equation symbols.namesake Classical mechanics Harmonic function symbols Boundary value problem Physical and Theoretical Chemistry Linear combination Hamiltonian (quantum mechanics) |
| Zdroj: | International Journal of Quantum Chemistry. 111:2882-2897 |
| ISSN: | 0020-7608 |
| DOI: | 10.1002/qua.22569 |
| Popis: | The Schrodinger equation for the Hydrogen atom in spheroconal coordinates admits factorizable solutions, due to the fact that the Hamiltonian, the square of the angular momentum, and a linear combination of the squares of the Cartesian components of the angular momentum form a complete set of commuting operators. The linear combination defines the geometry of a family of elliptical cones, each one of which may serve as a confining boundary for the Hydrogen atom allowing the construction of its exact eigenfunctions expressed as the products of radial Laguerre polynomial functions and quasi-periodic Lame spheroconal harmonic functions in the elliptical cone coordinates. The boundary condition, requiring the vanishing of the wave function at the confining elliptical cone, introduces noninteger values of the angular momentum quantum label, as well as the breaking of the parity symmetry. Numerical results of the energy spectra, electric dipole moment, and pressure distribution of the Hydrogen atom are reported for different shapes and positions of the confining boundary. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011 |
| Databáze: | OpenAIRE |
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