Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Meaning of Non-Hermitian Operators in Quantum Mechanics -A conceptual review on the physical interpretation of non-Hermitian Hamiltonians

Dinesh Kumar

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.13140/rg.2.2.19955.59689

Related papers

Non-Hermitian Hamiltonians in Quantum Physics

Fabio Bagarello, Roberto Passante, Camillo Trapani

Springer proceedings in physics•Jan 1, 2016•111 citations

Conceptual aspects of \mathcal{P}\mathcal{T} -symmetry and pseudo-Hermiticity: a status report

Ali Mostafazadeh

We survey some of the main conceptual developments in the study of -symmetric and pseudo-Hermitian Hamiltonian operators that have taken place during the past 10 years or so. We offer a precise mathematical description of a quantum system and its representations that allows us to describe the idea of unitarization of a quantum system by modifying the inner product of the Hilbert space. We discuss the role and importance of the quantum-to-classical correspondence principle that provides the physical interpretation of the observables in quantum mechanics. Finally, we address the problem of constructing an underlying classical Hamiltonian for a unitary quantum system defined by an a priori non-Hermitian Hamiltonian.

arXiv:1008.4680•Physica Scripta•Aug 18, 2010•48 citations

The Black-Scholes Equation and Certain Quantum Hamiltonians

Juan M. Romero, Oswaldo Gonzalez-Gaxiola, J. Ruiz de Chávez +1 more

In this paper a quantum mechanics is built by means of a non-Hermitian momentum operator. We have shown that it is possible to construct two Hermitian and two non-Hermitian type of Hamiltonians using this momentum operator. We can construct a generalized supersymmetric quantum mechanics that has a dual based on these Hamiltonians. In addition, it is shown that the non-Hermitian Hamiltonians of this theory can be related to Hamiltonians that naturally arise in the so-called quantum finance.

arXiv:1002.1667•Feb 8, 2010•8 citations

Non-Hermitian Operators in Quantum Physics

Hynek Bíla

•May 11, 2009•9 citations

On non-Hermitian quantum mechanics.

Jared L. Peacock

The purpose of this dissertation is to review the salient features of non-Hermitian quantum mechanics. An introduction to Hermitian quantum mechanics is included to make this review as accessible as possible. Attempts at formulating a consistent physical theory are introduced, before examining non-Hermitian theories’ uses as convenient computational frameworks. Particular emphasis is placed on recent developments in open quantum systems that utilise non-Hermitian Hamiltonians. Chapter four introduces a logic that maps a non-Hermitian Hamiltonian onto a non-Hamiltonian algebra that has a Hermitian Hamiltonian. This was put forward by Sergi, who then goes on to show its application to a two level system. The time evolution is then derived in terms of the density matrix model. This system can then be used to analyse different types of decay such as coherence and population difference. This serves to illustrate the usefulness of the approach.

•Mar 19, 2014•1 citation

Quantum mechanics with a non-Hermitian Hamiltonian

Alexander N. Grigorenko

Physics Letters A•Jan 1, 1993•9 citations
We survey some of the main conceptual developments in the study of -symmetric and pseudo-Hermitian Hamiltonian operators that have taken place during the past 10 years or so. We offer a precise mathematical description of a quantum system and its representations that allows us to describe the idea of unitarization of a quantum system by modifying the inner product of the Hilbert space. We discuss the role and importance of the quantum-to-classical correspondence principle that provides the physical interpretation of the observables in quantum mechanics. Finally, we address the problem of constructing an underlying classical Hamiltonian for a unitary quantum system defined by an a priori non-Hermitian Hamiltonian.
The purpose of this dissertation is to review the salient features of non-Hermitian quantum mechanics. An introduction to Hermitian quantum mechanics is included to make this review as accessible as possible. Attempts at formulating a consistent physical theory are introduced, before examining non-Hermitian theories’ uses as convenient computational frameworks. Particular emphasis is placed on recent developments in open quantum systems that utilise non-Hermitian Hamiltonians. Chapter four introduces a logic that maps a non-Hermitian Hamiltonian onto a non-Hamiltonian algebra that has a Hermitian Hamiltonian. This was put forward by Sergi, who then goes on to show its application to a two level system. The time evolution is then derived in terms of the density matrix model. This system can then be used to analyse different types of decay such as coherence and population difference. This serves to illustrate the usefulness of the approach.