A family of complex potentials with real spectrum

We consider a two-parameter non hermitean quantum-mechanical hamiltonian that is invariant under the combined effects of parity and time reversal transformation. Numerical investigation shows that for some values of the potential parameters the hamiltonian operator supports real eigenvalues and localized eigenfunctions. In contrast with other PT symmetric models, which require special integration paths in the complex plane, our model is integrable along a line parallel to the real axis.Comment: Six figures and four table

Harmonic oscillator well with a screened Coulombic core is quasi-exactly solvable

In the quantization scheme which weakens the hermiticity of a Hamiltonian to its mere PT invariance the superposition V(x) = x^2+ Ze^2/x of the harmonic and Coulomb potentials is defined at the purely imaginary effective charges (Ze^2=if) and regularized by a purely imaginary shift of x. This model is quasi-exactly solvable: We show that at each excited, (N+1)-st harmonic-oscillator energy E=2N+3 there exists not only the well known harmonic oscillator bound state (at the vanishing charge f=0) but also a normalizable (N+1)-plet of the further elementary Sturmian eigenstates \psi_n(x) at eigencharges f=f_n > 0, n = 0, 1, ..., N. Beyond the first few smallest multiplicities N we recommend their perturbative construction.Comment: 13 pages, Latex file, to appear in J. Phys. A: Math. Ge

Quark Cluster Model Study of Isospin-Two Dibaryons

Based on a quark cluster model for the non-strange sector that reproduces reasonably well the nucleon-nucleon system and the excitation of the $\Delta$ isobar, we generate a nucleon-$\Delta$ interaction and present the predictions for the several isospin two channels. The only attractive channels are $0^+$ and $0^-$, but not attractive enough to generate a resonance. If a resonance is artificially generated and is required to have the observed experimental mass, then our model predicts a width that agrees with the experimental result.Comment: 12 pages, 5 poscript figures available under request. To appear in Phys. Rev.

Inversion of perturbation series

We investigate the inversion of perturbation series and its resummation, and prove that it is related to a recently developed parametric perturbation theory. Results for some illustrative examples show that in some cases series reversion may improve the accuracy of the results

Quasi-exactly solvable quartic potentials with centrifugal and Coulombic terms

PT symmetric complex potential V(r) = - r^4 + i a r^3 + b r^2 + i c r + i d/r + e/r^2 is studied. Arbitrarily large multiplets of its closed bound-state solutions with real energies are shown obtainable quasi-exactly (i.e., with a certain relationship between their charges and energies) from a single underlying finite-dimensional secular equation.Comment: 13 pages, 1 figure, submitted to J. Phys. A: Math. Ge

Matching method and exact solvability of discrete PT-symmetric square wells

Discrete PT-symmetric square wells are studied. Their wave functions are found proportional to classical Tshebyshev polynomials of complex argument. The compact secular equations for energies are derived giving the real spectra in certain intervals of non-Hermiticity strengths Z. It is amusing to notice that although the known square well re-emerges in the usual continuum limit, a twice as rich, upside-down symmetric spectrum is exhibited by all its present discretized predecessors.Comment: 25 pp, 3 figure

On the η\eta and η′\eta' Photoproduction Beam Asymmetry at High Energies

We show that, in the Regge limit, beam asymmetries in $\eta$ and $\eta'$ photoproduction are sensitive to hidden strangeness components. Under reasonable assumptions about the couplings we estimate the contribution of the $\phi$ Regge pole, which is expected to be the dominant hidden strangeness contribution. The ratio of the asymmetries in $\eta'$ and $\eta$ production is estimated to be close to unity in the forward region $0 < -t/\text{GeV}^2 \leq 1$ at the photon energy $E_\text{lab} = 9$~GeV, relevant for the upcoming measurements at Jefferson Lab.Comment: 9 pages, 4 figure