Discrete PT −symmetric square-well oscillators
نویسنده
چکیده
Exact solvability of the discretized N−point version of the PT −symmetric squarewell model at all N is pointed out. Its wave functions are found proportional to the classical Tshebyshev polynomials Uk cos θ) of a complex argument. A compact secular equation is derived giving the real spectrum of energies at all the non-Hermiticity strengths Z ∈ (−Zcrit(N), Zcrit(N)). In the limit Z → 0 the model degenerates to a Hermitian Hückel Hamiltonian. PACS 03.65.Ge, 02.60.Lj, 02.70.Bf, 31.15.Ct e-mail: [email protected]
منابع مشابه
Overcritical PT -symmetric square well potential in the Dirac equation
We study scattering properties of a PT -symmetric square well potential with real depth larger than the threshold of particle-antiparticle pair production as the time component of a vector potential in the Dirac equation. Spontaneous pair production inside the well becomes tiny beyond the strength at which discrete bound states with real energies disappear, consistently with a spontaneous break...
متن کاملOn the eigenvalues of some nonhermitian oscillators
We consider a class of one-dimensional nonhermitian oscillators and discuss the relationship between the real eigenvalues of PT-symmetric oscillators and the resonances obtained by different authors. We also show the relationship between the strong-coupling expansions for the eigenvalues of those oscillators. Comparison of the results of the complex rotation and the Riccati-Padé methods reveals...
متن کاملPt-symmetric Square Well and the Associated Susy Hierarchy
The PT-symmetric square well problem is considered in a SUSY framework when the coupling strength lies below the critical value where PT symmetry becomes spontaneously broken. We find SUSY partner potentials to exist admitting a hierarchy with energy levels depicting an unbroken SUSY situation. Such a hierarchy is a PT-symmetric analogue of the family of sec2-like potentials, to which it reduce...
متن کاملPt-symmetric Square Well and the Associated Susy Hierarchies
The PT-symmetric square well problem is considered in a SUSY framework. When the coupling strength Z lies below the critical value Z (crit) 0 where PT symmetry becomes spontaneously broken, we find a hierarchy of SUSY partner potentials, depicting an unbroken SUSY situation and reducing to the family of sec2-like potentials in the Z → 0 limit. For Z above Z 0 , there is a rich diversity of SUSY...
متن کاملPT symmetric pseudo-perturbation recipe
The pseudo-perturbative shifted l expansion technique PSLET is shown applicable in the non-Hermitian PT symmetric context. The construction of bound states for several PT symmetric potentials is presented, with special attention paid to V (r) = ir3 − α √ ir oscillators.
متن کامل