Anharmonic Oscillators with Infinitely Many Real Eigenvalues and PT-Symmetry

Generalized Nonanalytic Expansions, PT -Symmetry and Large-Order Formulas for Odd Anharmonic Oscillators

The concept of a generalized nonanalytic expansion which involves nonanalytic combinations of exponentials, logarithms and powers of a coupling is introduced and its use illustrated in various areas of physics. Dispersion relations for the resonance energies of odd anharmonic oscillators are discussed, and higher-order formulas are presented for cubic and quartic potentials.

Non-Hermitian matrix description of the PT −symmetric anharmonic oscillators

The PT −symmetric differential Schrödinger equation Hψ = Eψ with the operator H = H(x) = p + a x + i β x + c x + i δ x ≡ H∗(−x) on L2(−∞,∞) is studied. At a > 0 it is re-arranged as a linear algebraic diagonalization. With rigorous proof, our non-variational construction of bound states offers an infinite-dimensional analogue to the recent finite-dimensional quasi-exact solution available at th...

Infinitely Many Entire Solutions of an Elliptic System with Symmetry

Pt-symmetric Non-polynomial Oscillators and Hyperbolic Potential with Two Known Real Eigenvalues in a Susy Framework

Extending the supersymmetric method proposed by Tkachuk to the complex domain, we obtain general expressions for superpotentials allowing generation of quasiexactly solvable PT-symmetric potentials with two known real eigenvalues (the ground state and first-excited state energies). We construct examples, namely those of complexified non-polynomial oscillators and of a complexified hyperbolic po...

Queues with infinitely many servers

— In the time interval (0, oo) calls arrive in a téléphone exchange in accordance with a récurrent process. There are an unlimited number ofavailable Unes. The holding times are mutually independent and identically distributed positive rondom variables and are independent of the arrivai times. In this paper we détermine the limit distribution of the number of the busy Unes at the arrivai of the...