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)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
