Time of arrival from Bohmian flow

Gruebl, Gebhard; Rheinberger, Klaus

doi:10.1088/0305-4470/35/12/313

Cited by 30 publications

(28 citation statements)

References 16 publications

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“…A comprehensive review of studies on the arrival time problem until 2000 can be found in [22], while for more recent publications one can consult e.g. [147][148][149][150][151][152][153][154][155][156][157][158][159]. The concept of 'quantum delay time' (in scattering) was analyzed in [160][161][162].…”

Section: Arrival and Tunneling Timesmentioning

confidence: 99%

Energy–time and frequency–time uncertainty relations: exact inequalities

Dodonov

Додонов

2015

Phys. Scr.

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We give a short review of known exact inequalities that can be interpreted as 'energy-time' and 'frequency-time' uncertainty relations. In particular we discuss a precise form of signals minimizing the physical frequencytime uncertainty product. Also, we calculate the 'stationarity time' for mixed Gaussian states of a quantum harmonic oscillator, showing explicitly that pure quantum states are 'more fragile' than mixed ones with the same value of the energy dispersion. The problems of quantum evolution speed limits, time operators and measurements of energy and time are briefly discussed, too. This is our present to Margarita Alexandrovna and Vladimir Ivanovich Man'ko on occasion of their 75th birthdays. ‡ Heisenberg and Bohr used the symbols = or ∼ instead of . arXiv:1504.00862v1 [quant-ph] 3 Apr 2015Energy-time and frequency-time uncertainty relations: exact inequalities

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Section: Arrival and Tunneling Timesmentioning

confidence: 99%

Energy–time and frequency–time uncertainty relations: exact inequalities

Dodonov

Додонов

2015

Phys. Scr.

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“…To get a probability distribution from the current we have to clearly specify how to handle the crossings from behind the detector and the multiple crossings of the same trajectory. For example, one can count only the first time that every trajectory reaches the detector position, disregarding any further crossing, getting the so-called truncated current (Daumer et al, 1997;Grübl and Rheinberger, 2002).…”

Section: The Easy Derivation Again mentioning

confidence: 99%

The Role of the Probability Current for Time Measurements

Vona

Dürr

2015

Lecture Notes in Physics

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“…This subject remains mired in controversy, with various research groups proposing their own favorite candidates for the "time operator" while paying little attention to the proposals of the other groups. For an analysis of time measurements within the framework of Bohmian mechanics, see [20]; in this regard see also [57,58,59,47].…”

Section: The Extended Quantum Formalismmentioning

confidence: 99%

Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory

Dürr¹,

Zanghı̀

2012

Quantum Physics Without Quantum Philosophy

117

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Bohmian mechanics is the most naively obvious embedding imaginable of Schrödinger's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function ψ its configuration is typically random, with probability density ρ given by |ψ| 2 , the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, naturally emerges in Bohmian mechanics from the analysis of "measurements." This analysis reveals the status of operators as observables in the description of quantum phenomena, and facilitates a clear view of the range of applicability of the usual quantum mechanical formulas. * Dedicated to Elliott Lieb on the occasion of his 70th birthday. Elliott will be (we fear unpleasantly) surprised to learn that he bears a greater responsibility for this paper than he could possibly imagine. We would of course like to think that our work addresses in some way the concern suggested by the title of his recent talks, The Quantum-Mechanical World View: A Remarkably Successful but Still Incomplete Theory, but we recognize that our understanding of incompleteness is much more naive than Elliott's. He did, however, encourage us in his capacity as an editor of the Reviews of Modern Physics to submit a paper on the role of operators in quantum theory. That was 12 year ago. Elliott is no longer an editor there and the paper that developed is not quite a review.

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Time of arrival from Bohmian flow

Cited by 30 publications

References 16 publications

Energy–time and frequency–time uncertainty relations: exact inequalities

Energy–time and frequency–time uncertainty relations: exact inequalities

The Role of the Probability Current for Time Measurements

Quantum Equilibrium and the Role of Operators as Observables in Quantum Theory

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