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Revista mexicana de física E
Print version ISSN 1870-3542
Abstract
DE VINCENZO, S. Impenetrable barriers in quantum mechanics. Rev. mex. fís. E [online]. 2008, vol.54, n.1, pp.1-6. ISSN 1870-3542.
We derive the expression V(x) u(x) = cδ (x - a) + v(x) u(x) (where V(x) is the potential, u(x) the wave function, c a constant and v(x) a finite potential function for x < a), which is present in the one-dimensional Schrödinger equation on the whole real line when we have an impenetrable barrier at x > a, that is, an infinite step potential there. By studying the solution of this equation, we identify, connect and discuss three different Hamiltonian operators that describe the barrier. We extend these results by constructing an infinite square-well potential from two impenetrable barriers
Keywords : Quantum mechanics; Schrödinger equation; impenetrable barriers.