We develop a new conception for the quantum mechanical arrival time distribution from the perspective of Bohmian mechanics. A detection probability for detectors sensitive to quite arbitrary spacetime domains is formulated. Basic positivity and monotonicity properties are established. We show that our detection probability improves and generalises an earlier proposal by Leavens and McKinnon. The difference between the two notions is illustrated through application to a free wave packet.
Bell's theorem prevents local Kolmogorov-simulations of the singlet state of two spin-1/2 particles. We derive a positive lower bound for the L 2 -distance between the quantum mechanical spin singlet anticorrelation function cos and any of its classical approximants C formed by the stationary autocorrelation functions of mean-squarecontinuous, 2π-periodic, ±1-valued, stochastic processes. This bound is given by C − cos ≥ 1 − 8 π 2 / √ 2 ≈ 0.133 95.
A solution ψ to Schrödinger's equation needs some degree of regularity in order to allow the construction of a Bohmian mechanics from the integral curves of the velocity field ( ψ/mψ) . In the case of one specific non-differentiable weak solution Ψ we show how Bohmian trajectories can be obtained for Ψ from the trajectories of a sequence Ψn → Ψ. (For any real t the sequence Ψn (t, •) converges strongly.) The limiting trajectories no longer need to be differentiable. This suggests a way how Bohmian mechanics might work for arbitrary initial vectors Ψ in the Hilbert space on which the Schrödinger evolution Ψ → e −iht Ψ acts.
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