Modified Hellmann Feynman Theorem
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912302360428544 |
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| author | Hajong, Gaurav Mandal, Bhabani Prasad |
| author_facet | Hajong, Gaurav Mandal, Bhabani Prasad |
| contents | We review the well-known Hellmann Feynman Theorem (HFT), originally developed for Hermitian systems to facilitate the calculation of forces among the molecules. Our work extends this foundational theorem to the domain of non-Hermitian quantum mechanics, in particular the PT symmetric non-Hermitian quantum physics. We derive a modified form of the HFT (MHFT) which holds good for both PT broken, unbroken phases and even at the exceptional point of the theory as demonstrated with help of a discrete and a continumm model. Since a PT-symmetric Hamiltonian admits biorthonormal set of eigenvectors, a more appropriate inner product known as the G inner product is defined, based on which, the system in the unbroken phase can be shown to satisfy unitary time evolution, while a system in broken phase does not. We show here that the MHFT obtained is valid for both these situations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00433 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modified Hellmann Feynman Theorem Hajong, Gaurav Mandal, Bhabani Prasad Quantum Physics We review the well-known Hellmann Feynman Theorem (HFT), originally developed for Hermitian systems to facilitate the calculation of forces among the molecules. Our work extends this foundational theorem to the domain of non-Hermitian quantum mechanics, in particular the PT symmetric non-Hermitian quantum physics. We derive a modified form of the HFT (MHFT) which holds good for both PT broken, unbroken phases and even at the exceptional point of the theory as demonstrated with help of a discrete and a continumm model. Since a PT-symmetric Hamiltonian admits biorthonormal set of eigenvectors, a more appropriate inner product known as the G inner product is defined, based on which, the system in the unbroken phase can be shown to satisfy unitary time evolution, while a system in broken phase does not. We show here that the MHFT obtained is valid for both these situations. |
| title | Modified Hellmann Feynman Theorem |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2504.00433 |