Izvestiya of Saratov University.


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Tsoy V. I. Dynamics in Measurements of the Non-Relativistic Particle Coordinates. Izvestiya of Saratov University. Physics , 2020, vol. 20, iss. 4, pp. 299-305. DOI: 10.18500/1817-3020-2020-20-4-299-305

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Dynamics in Measurements of the Non-Relativistic Particle Coordinates

Tsoy Valery Ivanovich, Saratov State University

Background and Objectives: There are a few different ways to change the quantum mechanical wave function. One is the continuous evolution according to the Schrodinger equation; the others are the collapse provided by strong measurements and the weak continuous measurement. The question arises: Can the strong measurement be considered as a dynamical process. Methods: To answer the question, a dynamic model is proposed to simulate numerically the measurement of the coordinates of quantum particles. By measuring the coordinate, we mean the capture of a particle in a narrow box and the excitation of the stationary wave function in it. We consider the amplitude of the probability of transition to a stationary state as a wave function, and the non-stationary Schrodinger equation is solved using this initial function. The transition to a stationary state was modeled as a gated process. Results and Conclusion: It is shown that when measuring coordinates, along with the instant collapse, there are cases when the measurement takes a short but finite time. In particular, the projective measurement of the coordinate of one of the entangled particles takes some time and is accompanied by the correlation in the probability density of the particles coordinates. Moreover, the correlation is lost over time.

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