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Exactly Solvable Generalized Quantum Harmonic Oscillators Related With the Classical Orthogonal Polynomials
(Izmir Institute of Technology, 2016) Çayiç, Zehra; Atılgan Büyükaşık, Şirin; Atılgan Büyükaşık, Şirin; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
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.

Master Degree / Yüksek Lisans Tezleri