On the nondegeneracy theorem for a particle in a box
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| Format: | Artículo científico |
| Langue: | en |
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Sociedade Brasileira de Física
2008
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| _version_ | 1876486059114627072 |
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| author | Salvatore De Vincenzo |
| author_facet | Salvatore De Vincenzo |
| contents | On the nondegeneracy theorem for a particle in a box Salvatore De Vincenzo Física, Astronomía y Matemáticas Time Quantum Mechanics Particle in a box reversal invariance Nondegeneracy theorem We present some essential results for the Hamiltonian of a particle in a box. We discuss the invariance of this operator under time-reversal T, 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 T-invariant but "confining" (i.e., the particle is in a real impenetrable box). If the boundary conditions are not T-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 T-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. 2008 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46413552009 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.3A Vol.38 |
| format | Artículo científico |
| id | redalyc_46413552009 |
| institution | Redalyc |
| language | en |
| publishDate | 2008 |
| publisher | Sociedade Brasileira de Física |
| spellingShingle | On the nondegeneracy theorem for a particle in a box Salvatore De Vincenzo Física, Astronomía y Matemáticas Time Quantum Mechanics Particle in a box reversal invariance Nondegeneracy theorem On the nondegeneracy theorem for a particle in a box Salvatore De Vincenzo Física, Astronomía y Matemáticas Time Quantum Mechanics Particle in a box reversal invariance Nondegeneracy theorem We present some essential results for the Hamiltonian of a particle in a box. We discuss the invariance of this operator under time-reversal T, 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 T-invariant but "confining" (i.e., the particle is in a real impenetrable box). If the boundary conditions are not T-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 T-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. 2008 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46413552009 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.3A Vol.38 |
| title | On the nondegeneracy theorem for a particle in a box |
| topic | Física, Astronomía y Matemáticas Time Quantum Mechanics Particle in a box reversal invariance Nondegeneracy theorem |
| url | https://www.redalyc.org/articulo.oa?id=46413552009 |