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## Pseudo-Hermitian Representation of Quantum Mechanics

- A. Mostafazadeh
- Mathematics
- 31 October 2008

A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a… Expand

## Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian

- A. Mostafazadeh
- Physics
- 1 July 2001

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… Expand

## Pseudo-Hermiticity versus PT-symmetry III: Equivalence of pseudo-Hermiticity and the presence of antilinear symmetries

- A. Mostafazadeh
- Mathematics
- 4 March 2002

We show that a diagonalizable (non-Hermitian) Hamiltonian H is pseudo-Hermitian if and only if it has an antilinear symmetry, i.e., a symmetry generated by an invertible antilinear operator. This… Expand

## The Geometric Phase in Quantum Systems: Foundations, Mathematical Concepts, and Applications in Molecular and Condensed Matter Physics

- A. Bohm, A. Mostafazadeh, H. Koizumi, Q. Niu, J. Zwanziger
- Physics
- 12 June 2003

1. Introduction.- 2. Quantal Phase Factors for Adiabatic Changes.- 3. Spinning Quantum System in an External Magnetic Field.- 4. Quantal Phases for General Cyclic Evolution.- 5. Fiber Bundles and… Expand

## Exact PT-symmetry is equivalent to Hermiticity

- A. Mostafazadeh
- Physics, Mathematics
- 11 April 2003

We show that a quantum system possessing an exact antilinear symmetry, in particular PT-symmetry, is equivalent to a quantum system having a Hermitian Hamiltonian. We construct the unitary operator… Expand

## Time-dependent pseudo-Hermitian Hamiltonians defining a unitary quantum system and uniqueness of the metric operator

- A. Mostafazadeh
- Physics, Mathematics
- 13 June 2007

## Pseudo-Hermiticity versus PT-symmetry. II. A complete characterization of non-Hermitian Hamiltonians with a real spectrum

- A. Mostafazadeh
- Mathematics
- 12 October 2001

We give a necessary and sufficient condition for the reality of the spectrum of a non-Hermitian Hamiltonian admitting a complete set of biorthonormal eigenvectors.

## Spectral singularities of complex scattering potentials and infinite reflection and transmission coefficients at real energies.

- A. Mostafazadeh
- Mathematics, PhysicsPhysical review letters
- 28 January 2009

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## Quantum Brachistochrone problem and the geometry of the state space in pseudo-Hermitian quantum mechanics.

- A. Mostafazadeh
- PhysicsPhysical review letters
- 26 June 2007

A non-Hermitian operator with a real spectrum and a complete set of eigenvectors may serve as the Hamiltonian operator for a unitary quantum system provided that one makes an appropriate choice for… Expand

## Pseudo-Hermitian quantum mechanics with unbounded metric operators

- A. Mostafazadeh
- Physics, MathematicsPhilosophical Transactions of the Royal Society A…
- 28 March 2012

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