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

On the Pseudo-Hermiticity of General PT-Symmetric Standard Hamiltonians in One Dimension

Alí Mostafazadeh

Published Apr 8, 2002• 3 citations
OpenAlex

Related papers

Generalized $\eta$-Pseudo-Hermiticity generators: radially symmetric Hamiltonians

Omar Mustafa, S. Habib Mazharimousavi

•Jan 3, 2006•1 citation

η-Weak-Pseudo-Hermiticity Generators and Radially Symmetric Hamiltonians

Omar Mustafa, S. Habib Mazharimousavi

arXiv:hep-th/0601017•International Journal of Theoretical Physics•Jan 10, 2008•5 citations

On the eigenvalues and dynamics of non-Hermitian PT symmetric Hamiltonians in finite basis spaces

Chandan Kumar Mondal, Kaushik Maji, Sukhamoy Bhattacharyya

Physics Letters A•Dec 1, 2001•11 citations

PT-Symmetric Hamiltonians as couplings of dual pairs

Volodymyr Derkach, Philipp Schmitz, Carsten Trunk

In the seminal paper (Bender & Boettcher, 1998) a new view of quantum mechanics was proposed. This new view differs from the old one in that the restriction on the Hamiltonian to be Hermitian is relaxed: now the Hamiltonian is PT -symmetric. Here P is parity and T is time reversal. Since 1998, PT -symmetric Hamiltonians have been analyzed intensively by many authors. In Mostafazadeh (2002) PT -symmetry was embedded into the more general mathematical framework of pseudo-Hermiticity or, what is the same, self-adjoint operators in Kre˘ın spaces, see (Langer & Tretter, 2004; Azizov & Trunk, 2012; Hassi & Kuzhel, 2013; Leben & Trunk, 2019). For a general introduction to PT -symmetric quantum mechanics we refer to the overview paper of Mostafazadeh (2010) and to the books of Moiseyev (2011) and Bender (2019).

•Apr 20, 2021•0 citations

On the pseudo-Hermitian nondiagonalizable Hamiltonians

G. Scolarici, Luigi Solombrino

•Jan 1, 2003•0 citations

Pseudo-Hermiticity versus PT Symmetry: The structure responsible for the reality of the spectrum of a non-Hermitian Hamiltonian

Alí Mostafazadeh

We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT-symmetric non-Hermitian Hamiltonians studied in the literature belong to the class of pseudo-Hermitian Hamiltonians, and argue that the basic structure responsible for the particular spectral properties of these Hamiltonians is their pseudo-Hermiticity. We explore the basic properties of general pseudo-Hermitian Hamiltonians, develop pseudo-supersymmetric quantum mechanics, and study some concrete examples, namely the Hamiltonian of the two-component Wheeler-DeWitt equation for the FRW-models coupled to a real massive scalar field and a class of pseudo-Hermitian Hamiltonians with a real spectrum.

•Jul 1, 2001•4 citations
Generalized η\etaη-Pseudo-Hermiticity generators: radially symmetric Hamiltonians
In the seminal paper (Bender & Boettcher, 1998) a new view of quantum mechanics was proposed. This new view differs from the old one in that the restriction on the Hamiltonian to be Hermitian is relaxed: now the Hamiltonian is PT -symmetric. Here P is parity and T is time reversal. Since 1998, PT -symmetric Hamiltonians have been analyzed intensively by many authors. In Mostafazadeh (2002) PT -symmetry was embedded into the more general mathematical framework of pseudo-Hermiticity or, what is the same, self-adjoint operators in Kre˘ın spaces, see (Langer & Tretter, 2004; Azizov & Trunk, 2012; Hassi & Kuzhel, 2013; Leben & Trunk, 2019). For a general introduction to PT -symmetric quantum mechanics we refer to the overview paper of Mostafazadeh (2010) and to the books of Moiseyev (2011) and Bender (2019).
We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT-symmetric non-Hermitian Hamiltonians studied in the literature belong to the class of pseudo-Hermitian Hamiltonians, and argue that the basic structure responsible for the particular spectral properties of these Hamiltonians is their pseudo-Hermiticity. We explore the basic properties of general pseudo-Hermitian Hamiltonians, develop pseudo-supersymmetric quantum mechanics, and study some concrete examples, namely the Hamiltonian of the two-component Wheeler-DeWitt equation for the FRW-models coupled to a real massive scalar field and a class of pseudo-Hermitian Hamiltonians with a real spectrum.