Abstract
Exact quasi-classical asymptotic beyond WKB-theory and beyond Maslov canonical operator to the Colombeau solutions of the n-dimensional Schrodinger equation is presented. Quantum jumps nature is considered successfully. We pointed out that an explanation of quantum jumps can be found to result from Colombeau solutions of the Schrodinger equation alone without additional postulates.
Highlights
A number of experiments on trapped single ions or atoms have been performed in recent years [1]-[4]
We found exact quasi-classical asymptotic of the quantum averages with position variable with localized initial data
We pointed out that there existed limiting quantum trajectories given via Equation (1.3) with a jump. Such jump does not depend on any single measurement of particle position q (t ) at instant t and is obtained without any reference to a phenomenological master-equation in Lindblad’s form
Summary
A number of experiments on trapped single ions or atoms have been performed in recent years [1]-[4]. The physical interpretation of these asymptotic given below, shows that the answer is “yes” for the limiting quantum trajectories with localized initial data. If potential V ( x,t ) is a non-regular this is well known problem to represent solution of the Schrödinger Equations (2.1)-(2.2) via formulae (2.3), see [19]. We avoided this difficulty using contemporary Colombeau framework [16]-[18]. Using the inequality (2.7) Theorem 2.1 asserts again that corresponding solution of the Schrödinger Equations (2.8)-(2.9) exist and can be represented via formulae:. From Lemma 2.2 follows that stationary phase approximation is not a valid asymptotic approximation in the limit → 0 for a path-integral (2.14) and (2.18)
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