Self-adjoint Dirac type Hamiltonians in one space dimension with a mass jump

On Self-adjoint and J-self-adjoint Dirac-type Operators: A Case Study

We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schrödinger equation, of relevance to nonlinear optics. In addition to a study of Dirac and Hamiltonian systems, we also introduce the concept of Weyl–Titchmarsh half-line m-coefficients (and 2 ...

A Critical Case on the Dirac-Klein-Gordon Equations in one Space Dimension

We establish local and global existence results for a critical case of Dirac-Klein-Gordon equations in one space dimension, employing a null form estimate, a bilinear estimate and a fixed point argument. 0. Introduction and Main Results. In the present work, we like to study the Cauchy problem for the Dirac-Klein-Gordon equations. The unknown quantities are a spinor field ψ : R × R 7→ C and a s...

9 Oscillator representations for self - adjoint Calogero Hamiltonians

In the article arXiv:0903.5277 [quant-ph], we have presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V (x) = αx−2. In such a way, we have described all possible s.a. operators (s.a. Hamiltonians) associated with the formal differential expression Ȟ = −dx + αx−2 for the Calogero Hamiltonian. Here, we discuss a new...

Skew-self-adjoint discrete and continuous Dirac type systems: inverse problems and Borg-Marchenko theorems

New formulas on the inverse problem for the continuous skewself-adjoint Dirac type system are obtained. For the discrete skewself-adjoint Dirac type system the solution of a general type inverse spectral problem is also derived in terms of the Weyl functions. The description of the Weyl functions on the interval is given. BorgMarchenko type uniqueness theorems are derived for both discrete and ...

Rank one perturbations of self-adjoint operators