Hidden scale in quantum mechanics

Details Hidden scale in quantum mechanics Hidden scale in quantum mechanics

2007-08-06

arxiv.org/abs/0708.0707v1

Mod.Phys.Lett.A24:2203-2211,2009

Physics

High Energy Physics

High Energy Physics - Theory

4 pages, 5 figures

Scientific paper

10.1142/S0217732309030102

We show that the intriguing localization of a free particle wave-packet is possible due to a hidden scale present in the system. Self-adjoint extensions (SAE) is responsible for introducing this scale in quantum mechanical models through the nontrivial boundary conditions. We discuss a couple of classically scale invariant free particle systems to illustrate the issue. In this context it has been shown that a free quantum particle moving on a full line may have localized wave-packet around the origin. As a generalization, it has also been shown that particles moving on a portion of a plane or on a portion of a three dimensional space can have unusual localized wave-packet.

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