We derive a non-linear differential equation that must be satisfied by the quantum potential, in the context of the Madelung equations, in one dimension for a particular class of wave functions. In this case, we exhibit explicit conditions leading to the blow-up of the quantum potential of a free particle at the boundary of the compact support of the probability density.

Blow-up of the quantum potential for a free particle in one dimension

DEVILLANOVA, Giuseppe;FLORIO, Giuseppe;MADDALENA, Francesco
2013-01-01

Abstract

We derive a non-linear differential equation that must be satisfied by the quantum potential, in the context of the Madelung equations, in one dimension for a particular class of wave functions. In this case, we exhibit explicit conditions leading to the blow-up of the quantum potential of a free particle at the boundary of the compact support of the probability density.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/52325
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