AUTHOR(S): Semra Bayat Ozdemir, Metin Demiralp

TITLE 
KEYWORDS Anharmonic Exponential Oscillator, DifferentialDifference Equation, Variational Approximation, Twosided Rayleigh (Ostrowski) Quotient 
ABSTRACT This work focuses on the derivation of a solution methodology to exponential anharmonic oscillator system based on the expectation values. A differentialdifference equation is constructed from the second derivative of expectation value of the exponential analytic function. Rearranging the equation gives us an eigenvalue problem. But the derived operator is not selfadjoint. This makes it impossible to use classical definition of Rayleigh Quotient for expectation value of the operator. Twosided Rayleigh (or Ostrowski) Quotient considers both left and right eigenfunction of the nonselfadjoint operator and this definition of expectation value gives the energy value of the corresponding system. For the approximate eigenfunctions, the energy value is approximate. We construct the final expectation value equation for the operator. But the optimization process for finding the minimum approximate energy value isn’t analytically solvable. To validate the methodology, harmonic oscillator is studied at the end and an acceptable result is found with elementary approximations of eigenfuctions. Improvement of the approximations and solution to exponential anharmonic oscillator system are left as future work. 
Cite this paper Semra Bayat Ozdemir, Metin Demiralp. (2016) Approximation to Expectation Value of NonSelfadjoint Operator in Anharmonic Exponential Oscillator System with Use of TwoSided Rayleigh Quotient. International Journal of Theoretical and Applied Mechanics, 1, 170175 