Quantum-like picture for intrinsic, classical, arrival distributions

Abstract

We introduce a marginal, quantum-like picture for the arrival of classical quantities in which the representation vectors are the quantities that evolve and probability densities remain static. The representation functions can be seen as probe functions which are the evolution of delta functions with support on a curve in phase space, the time fronts. This procedure provides a classical analog as well as a clear physical interpretation of the 'time eigenstates' used in quantum systems.

Detection of a quantum particle on a lattice under repeated projective measurements

“…The measurement of the arrival time of a quantum mechanical particle in a given detection region is a longstanding and fundamental problem in quantum mechanics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In spite of much effort, the construction of a time operator has been found to be controversial [18].…”

A Method for Choosing an Initial Time Eigenstate in Classical and Quantum Systems

“…With this choice, we ensure that the initial F eigensurface intersects all of the constant G shells, and this eigensurface is a simple surface that can be generated easily. This method is particularly convenient in quantum mechanics because we now have an easy way to define a zero-time eigenstate and justifies the use of coordinate eigenstates as the initial time eigenstates for other potential functions besides the free particle case [2,3,[5][6][7]. The additional condition to be considered is the use of a coordinate eigenstate at one of the extremal points of the G function so that the time eigenstates have components with all of the energy eigenvalues.…”

“…As we observed in Equation (1), X F · ∇ and G, as well as X G · ∇ and F , are conjugate pairs. Therefore, X F · ∇ and X G · ∇ can be used to translate functions in phase space along the G or F directions as follows: [2][3][4] …”

Correspondence, Time, Energy, Uncertainty, Tunnelling, and Collapse of Probability Densities

“…The way of handling time in classical and quantum physics, as well as in other theories in physics, has been a subject of the interest of many researchers for a long time now (Aharonov et al, 1961, Muga et al, 1998, Muga & Leavens, 2000, Muga, JG, Sala-Mayato, R and Egusquiza, IL (ed), , 2008, Galapon, 2002, Galapon et al, 2004, Isidro, 2005, 2009, Delgado et al, 1997, Giannitrapani, 1997, Halliwell, 1999, Hegerfeldt et al, 2004, Kijowski, 1974, Kobe et al, 1993, Kochański et al, 1999, Leavens, 2002, León, 1997, Rovelli, 1990. We make use of those developments and further develop and apply those ideas in this chapter.…”