相关论文: A reality proof in PT-symmetric quantum mechanics

A connection between integrable quantum field theory and the spectral theory of ordinary differential equations is reviewed, with particular emphasis being given to its relevance to certain problems in PT-symmetric quantum mechanics.

The physical condition that the expectation values of physical observables are real quantities is used to give a precise formulation of PT-symmetric quantum mechanics. A mathematically rigorous proof is given to establish the physical…

We review a surprising correspondence between certain two-dimensional integrable models and the spectral theory of ordinary differential equations. Particular emphasis is given to the relevance of this correspondence to certain problems in…

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…

It is generally assumed that a Hamiltonian for a physically acceptable quantum system (one that has a positive-definite spectrum and obeys the requirement of unitarity) must be Hermitian. However, a PT-symmetric Hamiltonian can also define…

We show that and how the Coulomb potential can be regularized and solved exactly at the imaginary couplings. The new spectrum of energies is real and bounded as expected, but its explicit form proves totally different from the usual…

A class of non-selfadjoint, $\PT$-symmetric operators is identified similar to a self-adjoint one, thus entailing the reality of the spectrum. The similarity transformation is explicitly constructed through the method of the quantum normal…

We investigate complex PT-symmetric potentials, associated with quasi-exactly solvable non-hermitian models involving polynomials and a class of rational functions. We also look for special solutions of intertwining relations of SUSY…

We construct an isospectrum systems in terms of a real and complex potential to show that the underlying PT symmetric Hamiltonian possesses a real spectrum which is shared by its real partner.

During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…

The recently proposed PT-symmetric quantum mechanics works with complex potentials which possess, roughly speaking, a symmetric real part and an anti-symmetric imaginary part. We propose and describe a new exactly solvable model of this…

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…

We reflect real spectra of new logarithmic model PT-symmetry operators with singular and non-singular in nature. We also notice that iso-spectral nature between inverted and non-inverted logarithmic PT-symmetric potentials. Present…

We suggest a general ansatz for the energy-eigenstates when a complex one-dimensional PT-symmetric potential possesses real discrete spectrum. Several interesting features of PT-symmetric quantum mechanics have been brought out using this…

Recently, it has been argued [arXiv:1111.6597, arXiv:1005.5173] that different quantum states do necessarily correspond to different elements of reality, under the assumption that quantum mechanics is correct and that measurement settings…

We show how in PT-symmetric 2J-level quantum systems the assumption of an upside-down symmetry (or duality) of their spectra simplifies their classification based on the non-equivalent pairwise mergers of the energy levels.

This article reviews a recently-discovered link between integrable quantum field theories and certain ordinary differential equations in the complex domain. Along the way, aspects of PT-symmetric quantum mechanics are discussed, and some…

Brief review is given of my recent results on solvable models within the so called PT symmetric version of quantum mechanics.

We study the physical content of the PT-symmetric complex extension of quantum mechanics as proposed in Bender et al, Phys. Rev. Lett. 80, 5243 (1998) and 89, 270401 (2002), and show that as a fundamental probabilistic physical theory it is…

$PT$ symmetric quantum mechanics for a particle trapped by the generalized non-Hermitian harmonic oscillator potential is studied. It is shown that energy and the expectation value of the position operator $x$ can not be real…