An efficient prescription to find the eigenfunctions of point interactions Hamiltonians

A prescription invented a long time ago by Case and Danilov is used to get the wave function of point interactions in two and three dimensions.Comment: 6 page

Comment on ``Validity of Feynman's prescription of disregarding the Pauli principle in intermediate states''

In a recent paper Coutinho, Nogami and Tomio [Phys. Rev. A 59, 2624 (1999); quant-ph/9812073] presented an example in which, they claim, Feynman's prescription of disregarding the Pauli principle in intermediate states of perturbation theory fails. We show that, contrary to their claim, Feynman's prescription is consistent with the exact solution of their example.Comment: 1 pag

The time-dependent Schrödinger equation: the need for the Hamiltonian to be self-adjoint

We present some simple arguments to show that quantum mechanics operators are required to be self-adjoint. We emphasize that the very definition of a self-adjoint operator includes the prescription of a certain domain of the operator. We then use these concepts to revisit the solutions of the time-dependent Schroedinger equation of some well-known simple problems - the infinite square well, the finite square well, and the harmonic oscillator. We show that these elementary illustrations can be enriched by using more general boundary conditions, which are still compatible with self-adjointness. In particular, we show that a puzzling problem associated with the Hydrogen atom in one dimension can be clarified by applying the correct requirements of self-adjointness. We then come to Stone\'s theorem, which is the main topic of this paper, and which is shown to relate the usual definitions of a self-adjoint operator to the possibility of constructing well-defined solutions of the time-dependent Schrödinger equation.Conselho Nacional de Desenvolvimento Cientí fico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

Dirac and Majorana heavy neutrinos at LEP II

The possibility of detecting single heavy Dirac and Majorana neutrinos at LEP II is investigated for heavy neutrino masses in the range $M_N=(\sqrt s/2, \sqrt s)$. We study the process $e^+e^- \longrightarrow \nu_{\ell} \ell q_i \bar q_j$ as a clear signature for heavy neutrinos. Numerical estimates for cross sections and distributions for the signal and the background are calculated and a Monte Carlo reconstruction of final state particles after hadronization is presented.Comment: 4 pages, 8 figure