Computational approach to the quantum Zeno effect: Position measurements

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Abstract
We present computational results of quantum-mechanical sequential measurements of a single dynamical variable (position) in a barrier penetration system. Our model is based on a well-rounded two-minima potential with a particle initially located on one side of the barrier. First we allow the particle wave function to propagate without further disturbance and calculate its barrier penetration time, then we perform measurements of the particle’s position and contrast the barrier penetration time T with the results for the undisturbed system. The time-dependent Schrödinger equation for the problem was solved using fast-Fourier-transform techniques. The barrier penetration time was found to depend on (1) the type of measurement made, (2) the strength of the interaction of the system with the meter, (3) the rate at which the measurements were performed, and (4) the precision of the meter (which in our model is related to the width of the meter’s wave function). We find no evidence in support of the Zeno effect. However, by using a caricature of quantum mechanics we can obtain results similar to the Zeno effect.

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