Related papers: Anti-$\mathcal{PT}$ Transformations And Complex No…
Witten's supersymmetric quantum mechanics may incorporate potentials with strong singularities after their appropriate regularization. This was proposed by Das and Pernice [Nucl. Phys. B 561 (1999) 357 and arXiv: hep-th/0207112]. We suggest…
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 relating an arbitrary non-Hermitian…
In the popular ${\cal PT}-$symmetry-based formulation of quantum mechanics of closed systems one can build unitary models using non-Hermitian Hamiltonians (i.e., $H \neq H^\dagger$) which are Hermitizable (so that one can write,…
In this project, we will develop the foundations of quantum mechanics using the methods of supersymmetry. We will discuss the use of the superpotential to derive the supersymmetric partner of a potential in one dimension, and explore…
Non-Hermitian systems, with symmetric or antisymmetric Hamiltonians under the parity-time ($\mathcal{PT}$) operations, can have entirely real eigenvalues. This fact has led to surprising discoveries such as loss-induced lasing and…
Electromagnetic materials possessing parity-time symmetry have received significant attention since it was discovered that the eigenmodes of these materials possess either real-frequency eigenvalues or the eigenfrequencies appear in…
The Lewis and Riesenfeld method has been investigated, by Ramos et al in Ref.[1], for quantum systems governed by time-dependent PT symmetric Hamiltonians and particularly where the quantum system is a particle submitted to action of a…
Many indefinite-metric (often called pseudo-Hermitian or PT-symmetric) quantum models H prove "physical" (i.e., Hermitian with respect to an innovated, ad hoc scalar product) inside a characteristic domain of parameters D. This means that…
We construct a family of hermitian potentials in 1D quantum mechanics that converges in the zero-range limit to a $\delta$ interaction with an energy-dependent coupling. It falls out of the standard four-parameter family of pointlike…
We introduce generalized versions of complex Scarf and Morse-type potentials that con- tain energy-dependent parameters. PT -symmetry and pseudo-hermiticity of the associated quantum systems are discussed, and a modified orthogonality…
Parity-Time (PT) symmetric quantum mechanics is a complex extension of conventional Hermitian quantum mechanics in which physical observables possess a real eigenvalue spectrum. However, an experimental demonstration of the true quantum…
I will provide a pedagogical introduction to non-Hermitian quantum systems that are PT-symmetric, that is they are left invariant under a simultaneous parity transformation (P) and time-reversal (T). I will explain how generalised versions…
The potential -x^4, which is unbounded below on the real line, can give rise to a well-posed bound state problem when x is taken on a contour in the lower-half complex plane. It is then PT-symmetric rather than Hermitian. Nonetheless it has…
A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space-time reflection symmetry (PT symmetry). Thus, there are infinitely many new…
Based on some results on reparmetrisation of time in Hamiltonian path integral formalism, a pseudo time formulation of operator formalism of quantum mechanics is presented. Relation of reparametrisation of time in quantum with super…
In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here, in contrast, that PT-symmetric quantum mechanics is fully…
Non-Hermitian Hamiltonians, and particularly parity-time (PT) and anti-PT symmetric Hamiltonians, play an important role in many branches of physics, from quantum mechanics to optical systems and acoustics. Both the PT and anti-PT…
Parity-time ($\mathcal{PT}$) symmetric systems are classical, gain-loss systems whose dynamics are governed by non-Hermitian Hamiltonians with exceptional-point (EP) degeneracies. The eigenvalues of a $\mathcal{PT}$-symmetric Hamiltonian…
Over the past decade, non-Hermitian, $\mathcal{PT}$-symmetric Hamiltonians have been investigated as candidates for both, a fundamental, unitary, quantum theory, and open systems with a non-unitary time evolution. In this paper, we…
The Hermiticity axiom of quantum mechanics guarantees that the energy spectrum is real and the time evolution is unitary (probability-preserving). Nevertheless, non-Hermitian but $\mathcal{PT}$-symmetric Hamiltonians may also have real…