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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
Two definitions of the electric polarizability of a bound system in relativistic quantum theory
For the electric polarizability of a bound system in relativistic quantum
theory, there are two definitions that have appeared in the literature. They
differ depending on whether or not the vacuum background is included in the
system. A recent confusion in this connection is clarified
Validity of Feynman's prescription of disregarding the Pauli principle in intermediate states
Regarding the Pauli principle in quantum field theory and in many-body
quantum mechanics, Feynman advocated that Pauli's exclusion principle can be
completely ignored in intermediate states of perturbation theory. He observed
that all virtual processes (of the same order) that violate the Pauli principle
cancel out. Feynman accordingly introduced a prescription, which is to
disregard the Pauli principle in all intermediate processes. This ingeneous
trick is of crucial importance in the Feynman diagram technique. We show,
however, an example in which Feynman's prescription fails. This casts doubts on
the general validity of Feynman's prescription
Dirac's hole theory versus quantum field theory
Dirac's hole theory and quantum field theory are usually considered
equivalent to each other. For models of a certain type, however, the
equivalence may not hold as we discuss in this Letter. This problem is closely
related to the validity of the Pauli principle in intermediate states of
perturbation theory.Comment: No figure
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
Many-body system with a four-parameter family of point interactions in one dimension
We consider a four-parameter family of point interactions in one dimension.
This family is a generalization of the usual -function potential. We
examine a system consisting of many particles of equal masses that are
interacting pairwise through such a generalized point interaction. We follow
McGuire who obtained exact solutions for the system when the interaction is the
-function potential. We find exact bound states with the four-parameter
family. For the scattering problem, however, we have not been so successful.
This is because, as we point out, the condition of no diffraction that is
crucial in McGuire's method is not satisfied except when the four-parameter
family is essentially reduced to the -function potential.Comment: 8 pages, 4 figure
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