On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schroedinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations in detail. We show that they can be expressed as the sum of the identity and an integral Hilbert-Schmidt operator. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive the similar self-adjoint operator and also find the associated "charge conjugation" operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.Comment: 27 page

Versatile pulse programmer for pulsed nuclear magnetic resonance spectroscopy

A description of the sequence of events and the decisions leading to the design of a versatile pulse programmer for pulsed NMR are presented. Background and application information is discussed in order that the reader might better understand the role of the pulse programmer in a NMR spectrometer. Various other design approaches are presented as a basis for comparison. Specifications for this design are proposed, the hardware implementation of the specifications is discussed, and the software operating system is presented