MCQST2021 | A New Concept for the Momentum of a Particle in a Space (...) (Uwe Jens Wiese)

A New Concept for the Momentum of a Particle in a Space with Impenetrable Boundaries
Speaker: Uwe-Jens Wiese | University of Bern

Abstract
In a region of space with impenetrable boundaries, the standard quantum mechanical momentum operator is not self-adjoint and thus does not describe the physical momentum. A new momentum concept, that is both physically and mathematically satisfactory, leads to a doubling of the Hilbert space. Based upon the new concept, the uncertainty relation is generalized to a finite volume. Also the Ehrenfest theorem, which is otherwise not satisfied, holds for a particle in a box, when the new momentum concept is applied. In that case, bouncing Gaussian wave packets split into two separate packets before they merge again later, and the fractional revival manifests itself in the corresponding momentum space wave functions. The new momentum concept is applicable, for example, to particles in an optical box trap and to quantum dots.

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