The factorization method is a kind of basic technique that reduces the dynamic equation of a given system into a simple one that is easier to handle. Its underlying idea is to consider a pair of first order differential equations which can be obtained from a given second-order differential equation with boundary conditions. The factorization method is an operational procedure that enables us to answer questions about the given quantum system eigenvalue problems which are of importance for physicists. Generally speaking, we are able to apply this method to treat the most important eigenvalue problems in quantum mechanics. For example, the solutions can be obtained immediately once the second-order differential equations are factorized by means of the linear ladder operators. The complete set of normalized eigenfunctions can be generated by the successive action of the ladder operators on the key eigenfunctions, which are the exact solutions of the first order differential equation.
KeywordsHarmonic Oscillator Factorization Method Order Differential Equation Darboux Transformation Kepler Problem
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