Features of Quantum Mechanics on a Ring

TL;DR

This paper investigates the effects of barrier insertions in quantum particles on a ring, revealing that assumptions of locality and linearity in barrier operations are incompatible, with implications for quantum theory foundations.

Contribution

It demonstrates the incompatibility of locality and linearity assumptions during barrier insertions in quantum rings, challenging standard quantum mechanical interpretations.

Findings

Barrier insertion at a fixed node requires energy.

Linear maps cannot fully describe barrier insertions.

Locality and linearity assumptions are incompatible in this context.

Abstract

Aspects of quantum mechanics on a ring are studied. Either one or two impenetrable barriers are inserted at nodal and non-nodal points to turn the ring into either one or two infinite square wells. In the process, the wave function of a particle can change its energy, as it gets entangled with the barriers and the insertion points become nodes. Two seemingly innocuous assumptions representing locality and linearity are investigated. Namely, a barrier insertion at a fixed node needs no energy, and barrier insertions can be described by linear maps. It will be shown that the two assumptions are incompatible.