Point interactions in quantum mechanics

R. A. Minlos, Людвиг Дмитриевич Фаддеев

Florian A. Scheck

L. Mandeļ

It is pointed out that the electromagnetic interaction $\ensuremath{-}\stackrel{^}{\ensuremath{\mu}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{^}{E}$ between an atom and a field, in which the atom is modelled as a point dipole of moment $\stackrel{^}{\ensuremath{\mu}}$ interacting with the electric field $\stackrel{^}{E}$, is not strictly consistent with both quantum mechanics and Maxwell's equations. Quantum mechanics allows magnetic point dipoles but not electric point dipoles.

T. Frederico, A. Delfino, Lauro Tomio +1 more

We show how to derive fixed-point Hamiltonians in quantum mechanics from a proposed renormalization group invariance approach that relies in a subtraction procedure at a given energy scale. The scheme is valid for arbitrary interactions that originally contain point-like singularities (as the Dirac-delta and/or its derivatives). One example of diagonalization of a fixed-point Hamiltonian illustrates the procedure for an interaction that contains regular and singular parts. In another example, the fixed point Hamiltonian is derived for the case of higher order singularities in the interaction.

Francisco Antônio Bezerra Coutinho, Yukihisa Nogami, J Fernando Perez

It is known that there is a four-parameter family of point interactions in one-dimensional quantum mechanics. We point out that, as far as physics is concerned, it is sufficient to use three of the four parameters. The fourth parameter is redundant. The apparent violation of time-reversal invariance in the presence of the fourth parameter is an artifact.