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
Keywords
Related Articles
- EP ID EP121510
- DOI -
- Views 137
- Downloads 0
Decompositions of Some Types of Supra Soft Sets and Soft Continuity
In this paper we introduce the notion of supra soft topological spaces. We extend the notion of -operation, pre-open soft sets, -open soft sets, semi-open soft sets and -open soft sets to such spaces and study their prop...
Bootstrap Testing for Long Range Dependence
The presence of long-memory or long-range dependence (LRD) in a stochastic process has important consequences in statistical inferences. Lo develops a robust test for detecting the existence of LRD and derives its asympt...
n ∗∗݃-Closed sets, ߙ∗∗݃- Continuity and ߙ∗∗݃- Homeomorphisms in Intuitionistic Fuzzy Topological Space
In this paper, we introduce and study the notions of intuitionistic fuzzy હ∗∗-closed sets, intuitionistic fuzzy હ∗∗-continuity, intuitionistic fuzzy હ∗∗-open mapping, intuitionistic fuzzy હ ∗∗-closed mapping,...
Distance r-Coloring and Distance r-Dominator Coloring number of a graph
Given a positive integer r, two vertices u,v V(G) are r-independent if d(u,v) > r. A partition of V(G) jnto r-independent set is called distance r-coloring . A study of distance r-coloring and distance r-dominator col...
Boolean Algebras of Pre A*-Algebra
In this paper, we obtain Boolean algebras , from Pre A*-algebra , and proved that , and are isomorphic to each other