Reality PT

A reality proof in PT -symmetric quantum mechanics

led Bender and Boettcher to conjecture that under suitable boundary conditions the spectrum of (1) was entirely real and positive provided M ≥ 1 [2]. Bender and Boettcher also noticed the relevance of PT -symmetry [2,3] to these problems. For all M , the potentials V (x) = −(ix)2M are invariant under the combined action of parity and time reversal, and this implies the eigenvalues are either re...

Spectral equivalences , Bethe Ansatz equations , and reality properties in PT - symmetric quantum mechanics

The one-dimensional Schrödinger equation for the potential x + αx + l(l+ 1)/x has many interesting properties. For certain values of the parameters l and α the equation is in turn supersymmetric (Witten), quasi-exactly solvable (Turbiner), and it also appears in Lipatov’s approach to high energy QCD. In this paper we signal some further curious features of these theories, namely novel spectral ...

On the Reality of the Eigenvalues for a Class of Pt -symmetric Oscillators

We study the eigenvalue problem −u′′(z) − [(iz) + P (iz)]u(z) = λu(z) with the boundary conditions that u(z) decays to zero as z tends to infinity along the rays arg z = − 2 ± 2π m+2 , where P (z) = a1z m−1 + a2z m−2 + · · ·+ am−1z is a real polynomial and m ≥ 2. We prove that if for some 1 ≤ j ≤ m 2 , we have (j − k)ak ≥ 0 for all 1 ≤ k ≤ m− 1, then the eigenvalues are all positive real. We th...

Pt Jet

Pt Jet