| Revista: | Brazilian journal of physics |
| Base de datos: | PERIÓDICA |
| Número de sistema: | 000403310 |
| ISSN: | 0103-9733 |
| Autors: | Vincenzo, Salvatore de1 |
| Institucions: | 1Universidad Central de Venezuela, Facultad de Ciencias, Caracas, Distrito Federal. Venezuela |
| Any: | 2008 |
| Període: | Sep |
| Volum: | 38 |
| Número: | 3A |
| Paginació: | 355-361 |
| País: | Brasil |
| Idioma: | Inglés |
| Tipo de documento: | Artículo |
| Enfoque: | Analítico |
| Resumen en inglés | We present some essential results for the Hamiltonian of a particle in a box. We discuss the invariance of this operator under time-reversal Tˆ, the possibility of choosing real eigenfunctions for it and the degeneracy of its energy eigenvalues. Once these results have been presented, we introduce the usual nondegeneracy theorem and discuss some issues surrounding it. We find that the nondegeneracy theorem is true if the boundary conditions are Tˆ-invariant but "confining" (i.e., the particle is in a real impenetrable box). If the boundary conditions are not Tˆ-invariant (belonging to a family of so-called “not confining” boundary conditions), the respective eigenfunctions are strictly complex and there is no degeneracy. Consistently, we verify the validity of the theorem also in this case. Finally, if the boundary conditions are also Tˆ-invariant, but “not confining”, then we can have degeneracy in the energy levels only if the respective eigenfunctions can be specifically written as complex. We find that the nondegeneracy theorem fails in these cases. If the respective eigenfunctions can be written as only real, then we do not have degeneracy and the nondegeneracy theorem is true |
| Disciplines | Física y astronomía, Matemáticas |
| Paraules clau: | Física de partículas y campos cuánticos, Matemáticas aplicadas, Mecánica cuántica, Hamiltonianos, Partícula en una caja |
| Keyword: | Physics and astronomy, Mathematics, Particle physics and quantum fields, Applied mathematics, Quantum mechanics, Hamiltonians, Particle in a box |
| Text complet: | Texto completo (Ver PDF) |
