Axiomatic foundation of quantum measurements and survival effect

• URL: http://arxiv.org/abs/1712.06999v2
• Date: Fri, 30 Aug 2024 23:04:37 GMT
• Title: Axiomatic foundation of quantum measurements and survival effect
• Authors: Vladimir I. Kruglov,
• Abstract summary: The measurement theory for observable with continuous spectrum is given in a rigged Hilbert space. The Postulates of axiomatic theory yield the survival effect which violates the Heisenberg uncertainty relation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The axiomatic theory of quantum first-kind measurements is developed in a rigorous form based on five Postulates. The measurement theory for observable with continuous spectrum is given in a rigged Hilbert space. This approach also describes the measurements with non-ideal initial conditions. It yields the survival effect in the position measurement of the particles. It is also found that there is no such survival effect in the momentum measurement of the particles. These Postulates of axiomatic theory yield the survival effect which violates the Heisenberg uncertainty relation. This theoretical result is demonstrated by the wave function with minimum of position and momentum uncertainty of the particle. The survival effect leads to essential corrections for the uncertainty relations. These modified uncertainty relations can also be used for the experimental verification of the survival measurement effect.

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