18319013
Non-Hermitian Hamiltonians with real and complex eigenvalues: An sl(2,C) approach
Potential algebras are extended from Hermitian to non-Hermitian Hamiltonians and shown to provide an elegant method for studying the transition from real to complex eigenvalues for a class of non-Hermitian Hamiltonians associated with the complex Lie algebra A$_1$.
18633717
CPT-conserving Hamiltonians and their nonlinear supersymmetrization using differential charge-operators C
A brief overview is given of recent developments and fresh ideas at the intersection of - and/or -symmetric quantum mechanics with supersymmetric quantum mechanics (SUSY QM). Within the framework of the resulting supersymmetric version of -symmetric quantum mechanics we study the consequences of the assumption that the "charge" operator is represented in a differential-operator form of the second or higher order. Besides the freedom allowed by the Hermiticity constraint for the operator , encouraging results are obtained in the second-order case. In particular, the integrability of intertwining relations proves to match the closure of our nonlinear (viz., polynomial) SUSY algebra. In a particular illustration, our form of -symmetric SUSY QM leads to a new class of non-Hermitian polynomial oscillators with real spectrum which turn out to be -asymmetric.
124385266
Mixing angles and decay constants of eta, eta-prime and eta(c)
2370482
A unified treatment of exactly solvable and quasi-exactly solvable quantum potentials
By exploiting the hidden algebraic structure of the Schrodinger Hamiltonian, namely the sl(2), we propose a unified approach of generating both exactly solvable and quasi-exactly solvable potentials. We obtain, in this way, two new classes of quasi-exactly solvable systems one of which is of periodic type while the other hyperbolic.
118783546
Masslessness of the up quark and eta-->3pi0 decay
120330577
Supersymmetry and conservation laws in the KdV system
The role of supersymmetry in the KdV-MKdV hierarchy of conservation laws is examined. Among all the fifth order evolution equations, the Lax equation turns out to be the only one which is mapped onto its modified partner through the pair of supersymmetric transformations.
120952330
The Zero-Energy Continuum Bound State of the Saito Potential
122098164
Analytic solutions in configuration space representation for scattering from a class of separable nonlocal potentials