Rauh, Alexander
(2017)
Quantum mechanics of rectilinear orbits of the CoulombKepler problem.
Advanced studies in theoretical physics, 11 (8).
pp. 365386.
ISSN 13131311
Abstract
Based on coherent states of the reversed harmonic oscillator, a wave function is proposed with the following three properties: (1) The mean values of position, r0, and velocity, v0, are parallel to the x axis; (2) The wave function is extended by a curve parameter w ≥ 0 such that, as a function of w, the mean values rw and vw describe a rectilinear orbit along the x axis with the mean initial values r0 and v0; (3) The mean energy is constant with respect to w by the leading order of the perturbation parameter ∈. For comparison, the classical onedimensional equation of motion is integrated. Exact analytical equivalence between classical and the ∈ = 0 quantum limit is found, both for positive and negative mean energy. The curve parameter w is in 11 correspondence with time t ≥ 0.
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