Exactly solvable generalized quantum harmonic oscillators related with the classical orthogonal polynomials
by
Çayiç, Zehra, author.
Title
:
Exactly solvable generalized quantum harmonic oscillators related with the classical orthogonal polynomials
Author
:
Çayiç, Zehra, author.
Personal Author
:
Çayiç, Zehra, author.
Physical Description
:
ix, 95 leaves:+ 1 computer laser optical disc.
Abstract
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In this thesis, we study exactly solvable generalized parametric oscillators related with the classical orthogonal polynomials of Hermite, Laguerre and Jacobi type. These quantum models with specific damping term, frequency and external forces are solved using Wei-Norman Lie algebraic approach. The exact form of the evolution operator is explicitly obtained in terms of two linearly independent homogeneous solutions and a particular solution of the corresponding classical equation of motion. Then, time evolution of wave functions and Glauber coherent states are constructed. Probability densities, expectation values and uncertainty relations are found and their properties are investigated according to the influence of the external forces. Besides, some examples with explicit solutions are given and their plots are constructed for the probability densities and uncertainty relations.
Subject Term
:
Harmonic oscillators.
Orthogonal polynomials.
Jacobi polynomials.
Hermite polynomials.
Laguerre polynomials.
Added Author
:
Atılgan Büyükaşık, Şirin
Added Corporate Author
:
İzmir Institute of Technology. Mathematics.
Added Uniform Title
:
Thesis (Master)--İzmir Institute of Technology:Mathematics.
İzmir Institute of Technology:Mathematics--Thesis (Master).
Electronic Access
:
Library | Material Type | Item Barcode | Shelf Number | Status |
---|
IYTE Library | Thesis | T001481 | QA404.5 .C385 2016 | Tez Koleksiyonu |
IYTE Library | Supplementary CD-ROM | ROM2597 | QA404.5 .C385 2016 EK.1 | Tez Koleksiyonu |