Modified Hellmann Feynman Theorem

• URL: http://arxiv.org/abs/2504.00433v1
• Date: Tue, 01 Apr 2025 05:31:30 GMT
• Title: Modified Hellmann Feynman Theorem
• Authors: Gaurav Hajong, Bhabani Prasad Mandal,
• Abstract summary: We review the well-known Hellmann Feynman Theorem (HFT)<n>We derive a modified form of the HFT which holds good for both PT broken, unbroken phases and even at the exceptional point of the theory.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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