Solutions of the Schrödinger equation by the heisenberg method

SOLUTIONS OF THE SCHRODINGER EQUATION BY THE HEISENBERG METHOD ( M.ScThesis) Mesut CANDARLI GAZI UNIVERSITY INSTUTE OF SCIENCE AND TECHNOLOGY Ocak 2002 ABSTRACT. In this study, it was introduced the energy eigenvalues of solvable potentials appeared by the Heisenberg Method.The operators of a and a+ were used for solving the eigenvalue of problems having different potentials from Harmonic Oscillator, and Schrödinger Equation was reduced to Whittakcr Equation (or hypergeometric equation), and then these two results were argued due to get a solvable potential set by a+a multiplication. As a result, it had been given the solution of the relativistic eigenvalue problem (H(E")1'n=Ell',FI1) when has new potentials. In additional, it had been showed to have this kind of eigenvalue equations that is related the Whittakcr function and then was used for generating the Hamiltonians were explanied by a+a multiplication. Science Code : 404. 03. 01 Key Words : Heisenberg Algebra, potentials, Schrödinger Equation, Exact solutions Page Number : 56 Adviser : Doç. Dr. Süleyman ÖZÇELİK