Operator of Time and Generalized Schrödinger Equation

Operator of Time and Generalized Schrödinger Equation

The equation describing the change of the state of the quantum system with respect to energy is introduced within the framework of the self-adjoint operator of time in nonrelativistic quantum mechanics. In this proposal, the operator of time appears to be the generator of the change of the energy, w...

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Main Author: Slobodan Prvanović
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2018/6290982
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spelling doaj-d4422280127449a3abeddacd52d36d892021-07-02T03:03:35ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/62909826290982Operator of Time and Generalized Schrödinger EquationSlobodan Prvanović0Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, SerbiaThe equation describing the change of the state of the quantum system with respect to energy is introduced within the framework of the self-adjoint operator of time in nonrelativistic quantum mechanics. In this proposal, the operator of time appears to be the generator of the change of the energy, while the operator of energy that is conjugate to the operator of time generates the time evolution. Two examples, one with discrete time and the other with continuous one, are given and the generalization of Schrödinger equation is proposed.http://dx.doi.org/10.1155/2018/6290982
collection DOAJ
language English
format Article
sources DOAJ
author Slobodan Prvanović
spellingShingle Slobodan Prvanović
Operator of Time and Generalized Schrödinger Equation
Advances in Mathematical Physics
author_facet Slobodan Prvanović
author_sort Slobodan Prvanović
title Operator of Time and Generalized Schrödinger Equation
title_short Operator of Time and Generalized Schrödinger Equation
title_full Operator of Time and Generalized Schrödinger Equation
title_fullStr Operator of Time and Generalized Schrödinger Equation
title_full_unstemmed Operator of Time and Generalized Schrödinger Equation
title_sort operator of time and generalized schrödinger equation
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2018-01-01
description The equation describing the change of the state of the quantum system with respect to energy is introduced within the framework of the self-adjoint operator of time in nonrelativistic quantum mechanics. In this proposal, the operator of time appears to be the generator of the change of the energy, while the operator of energy that is conjugate to the operator of time generates the time evolution. Two examples, one with discrete time and the other with continuous one, are given and the generalization of Schrödinger equation is proposed.
url http://dx.doi.org/10.1155/2018/6290982
work_keys_str_mv AT slobodanprvanovic operatoroftimeandgeneralizedschrodingerequation
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