Time-Evolution as an Operator in Hilbert Spaces with Applications in Quantum Mechanics
Journal Title: INTERNATIONAL JOURNAL OF MATHEMATICS TRENDS AND TECHNOLOGY - Year 2014, Vol 10, Issue 2
Abstract
The main aim of this article is to present the time-evolution as the unitary and self-adjoint operators on Hilbert spaces and to describe its application in the development of quantum mechanics. The initial value problems associated with the quantum mechanical Schrodinger equation, i (dψ(t))/dt=Hψ(t) in the Hilbert space is solved by the use of time-evolution. The importance of time-evolution is also seen as the operation of turning machine in quantum mechanics, which is regarded as the time-evolution of the machine control state. Time-evolution of a quantum mechanical system is observed to be unitary and self-adjoint operators of Hilbert space, since it corresponds to an observable, specifically energy position and momentum. It was observed that time-evolution of a quantum mechanical system is generated by a self-adjoint operator, called Hamiltonian, , expressed by the Schrodinger equation, above.
Authors and Affiliations
Dr. A. K. Choudhary , S. Musa , S. M. Nengem , Dr. S. K. Choudhary
SOME RESULTS ON KRONECKER PRODUCT OF TWO GRAPHS
We consider product graphs and recall the results associated to the product graphs. Paul M.Weichsel [3] defined the Kronecker product of graphs. He has proved a characterization for the product graphs to be connect...
Some New Families of Divisor Cordial Graphs
In this paper, the duplication of arbitrary vertex vk of cycle Cn (n ≥ 3),<Sn:Sn>, <Wn:Wn> , the graph obtained by joining two copies of cycle Wn by a path Pk (n ≥ 3), GvK1, where Gv denotes graph obtained by...
Anti Q-Fuzzy M-Subgroups Of Near Rings
In this paper, we introduce the notion of Q-fuzzification of M-subgroups in a near-ring and investigate some related properties. Characterization of Anti Q-fuzzy M- subgroups with respect to s-norm is given.
Innovation-Driven Sustainability Modelling for Poverty Alleviation Initiatives in Rural India: A Mathematical Approach
Today’s world is facing many severe challenges even though it had made encouraging progresses in economic and other respects. Agriculture is one of the important sources of economic and social growth of our country. In t...
Semipre Generalized Closed Mappings in Intuitionistic Fuzzy Topological Spaces
In this paper we introduce intuitionistic fuzzy semipre generalized closed mappings, intuitionistic fuzzy semipre generalized open mappings and intuitionistic fuzzy M-semipre generalized closed mappings and we stud...