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Spectral theory of difference equations and operators have been studied on for many years. In recent years, quantum calculus has received a lot of attention, so it has led to rapid development of the theory of q-difference equations and so, spectral analysis of these operators become popular and attractive for mathematicians. In this talk, I investigate the spectral analysis of second order q-difference equations with respect to their coefficients, boundary conditions and with respect to the properties of their Jost solution.