Quantum-mechanical models in \(R_ n\) associated with extensions of the energy operator in a Pontryagin space
This paper is concerned with a rigorous mathematical formulation of a quantum-mechanical model of a point interaction with nontrivial angular momentum transfer. The formal expression for such a model is \[ -\Delta +P_{\ell}((1/i)\partial)\delta (x), \] where \(P_{\ell}\) is a harmonic polynomial, homogeneous of degree \(\ell\). The operator to be constructed is a self-adjoint extension of \(H_ 0=-\Delta\) from the subset of functions which vanish in the neighborhood of \(x=0\). The extension is made from this space to a Pontryagin space \(\Pi_{\kappa}\), that is, a space with indefinite metric, having \(\kappa\) negative squares.
rigorous mathematical formulation of a quantum-mechanical model
of a point interaction with nontrivial angular momentum transfer
rigorous mathematical formulation of a quantum-mechanical model of a point interaction with nontrivial angular momentum transfer
scientific article; zbMATH DE number 4122641