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

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  • EP ID EP121510
  • DOI -
  • Views 146
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How To Cite

Dr. A. K. Choudhary, S. Musa, S. M. Nengem, Dr. S. K. Choudhary (2014). Time-Evolution as an Operator in Hilbert Spaces with Applications in Quantum Mechanics. INTERNATIONAL JOURNAL OF MATHEMATICS TRENDS AND TECHNOLOGY, 10(2), 60-69. https://europub.co.uk/articles/-A-121510