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arXiv · 2504.00433

Modified Hellmann Feynman Theorem

Gaurav Hajong·Bhabani Prasad Mandal
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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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Gaurav Hajong, Bhabani Prasad Mandal. 2025-04-01. Modified Hellmann Feynman Theorem. https://arxiv.org/abs/2504.00433

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