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Titre: | Some physical problems of pseudo-hermitian hamiltonians |
Auteur(s): | Rafa, Khadidja Ouarab, Sonia |
Mots-clés: | Hermiticity PT -symmetry Pseudo-Hermiticity Quasi-Hermiticity |
Date de publication: | 28-oct-2021 |
Editeur: | Université Blida 1 |
Résumé: | In this thesis we have discussed on one of the recent topics in physics, in particular in quantum mechanics, which is "the non-Hermitian Hamiltonians", and the conditions that make the spectra of these Hamiltonians real. Initially, the Hermeticity was a necessary and su cient condition for the reality of the Hamiltonian spectrum. Then a new quantum theory called the "PT -symmetry" started to emerge, this theory was developed in 1998 by Carl Bender and Stefan Boettcher, where they revealed the existence of a class of non-Hermitian Hamiltonians with real spectra. These Hamiltonians are invariant under the transformation of PT -symmetry, where P is the parity operator and T is the time reversal operator. A few years later, another alternative approach was developed in 2002 by Mostafazadeh who works on pseudo-Hermitian Hamiltonians and he showed that every Hamiltonian with a real spectrum is pseudo-Hermitian. We have found from an application on two examples of a pseudo-Hermitian Hamiltonians " shifted harmonic oscillator " and " cubic anharmonic oscillator " that the energy spectrum of these Hamiltonians are real and positive. Keywords: Hermiticity, PT -symmetry, Pseudo-Hermiticity, Quasi-Hermiticity. |
Description: | ill., Bibliogr. |
URI/URL: | http://di.univ-blida.dz:8080/jspui/handle/123456789/13301 |
Collection(s) : | Mémoires de Master |
Fichier(s) constituant ce document :
Fichier | Description | Taille | Format | |
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Rafa Khadidja et Ouarab Sonia.pdf | 3,52 MB | Adobe PDF | Voir/Ouvrir |
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