![]() In this paper, we will use a new approximation method called Delta method for finding the ground and excited energy state of stationary states. The application of the approximation methods to the study of stationary states consists of finding the energy eigenvalues and the eigenfunctions of a time-independent Hamiltonian that does not have exact solutions:ĭepending on the structure of, we can use any of the three methods mentioned above to find the approximate solutions to this eigenvalue problem. Unlike perturbation theory, the variational and WKB methods do not require the existence of a closely related Hamiltonian that can be solved exactly. The WKB method is useful for finding the energy eigenvalues and wave functions of systems for which the classical limit is valid. The variational method is particularly useful in estimating the energy eigenvalues of the ground state and the first few excited states of a system for which one has only a qualitative idea about the form of the wave function. So perturbation theory builds on the known exact solutions to obtain approximate solutions.īut, about those systems whose Hamiltonians cannot be reduced to an exactly solvable part plus a small correction, the variational method or the WKB approximation are considered. In the case where the deviation between the two problems is small, perturbation theory is suitable for calculating the contribution associated with this deviation this contribution is then added as a correction to the energy and the wave function of the exactly solvable Hamiltonians. Perturbation theory is based on the assumption that the problem we wish to solve is, in some sense, only slightly different from a problem that can be solved exactly. Three conventional approximation methods for studying the stationary states corresponding to time-indepen- dent Hamiltonians, are: perturbation theory, the variational method, and the WKB method. ![]() perturbation theory, the variational method, and the WKB method, Supersymmetry quantum mechanics -, Nikivorov-Uvarov method -, Romanovski polynomials in quantum mechanics -, etc. There are many methods for solving Schrodinger equation, i.e. Up to now, a variety of such methods have been developed, and each has its own area of applicability. So, in order to solve general problems, one must resort to approximation methods. Exact solutions of the Schrodinger equation exist only for a few idealized systems. Most problems encountered in quantum mechanics cannot be solved exactly. Received 10 December 2015 accepted 24 January 2016 published 27 January 2016
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