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(5.1) There are two possible ways to solve the corresponding time independent Schrödinger equation, the algebraic method, which will lead us to new important concepts, and the analytic method, which is the straightforward solving of a differential equation. The time dependent Schrodinger equation is one of 5 (or 6) postulates of quantum mechanics. Deriving time independent Schrdinger equation. In this chapter we will study the features of one of the most important potentials in physics, it's the harmonic oscillator potential which is included now in the Hamiltonian V (x) = mω 2 2 x 2. 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