Schrödinger operators with moving point perturbations and related solvable models of quantum mechanical systems (Q1381120)

The authors investigate spectral properties of self-adjoint operators of the form \(H(q,\mu)= H_0+ \mu\delta (x-q)\) in \(L^2(a,b)\), where \(H_0\) is a self-adjoint operator with a discrete spectrum which is the realisation of a formally self-adjoint differential expression of even order, \(\mu\in\mathbb{R} \setminus \{0\}\), \(q\in(a,b),- \infty\leq a<b \leq\infty\), and \(\delta\) is the Dirac delta function. This class of operators includes a number of examples arising in quantum mechanics. A complete analysis of the variation of the eigenvalues and eigenfunctions of \(H(q,\mu)\) with \(q\) is given.