Rafael Madrid

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We discuss the role of boundary conditions in determining the physical content of the solutions of the Schrödinger equation. We study the standing-wave, the “in,” the “out,” and the purely outgoing boundary conditions. As well, we rephrase Feynman’s +iε prescription as a time-asymmetric, causal boundary condition, and discuss the connection of Feynman’s +iε(More)
The Gamow (or resonance) states are the wave functions of resonances. These states are eigensolutions of the Schrödinger equation subject to a “purely outgoing boundary condition.” The Gamow states were introduced by Gamow [1] in 1928 to describe α decay (see also [2]). Some years later, in 1939, Siegert made use of the Gamow states to obtain a resonance(More)
This paper is a contribution to the problem of particle localization in non-relativistic Quantum Mechanics. Our main results will be (1) to formulate the problem of localization in terms of invariant subspaces of the Hilbert space, and (2) to show that the rigged Hilbert space incorporates particle localization in a natural manner. PACS numbers: 03.65.-w