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• W895726340 abstract "In quantum mechanics, the variation method is one way of finding approximations to the lowest energy Eigen state or ground state, and some excited states. The method consists in choosing a wave depending on one or more parameters, and finding the values of these parameters for which the expectation value of the energy is the lowest possible. The wave function obtained by fixing the parameters to such values is then an approximation to the ground state wave function, and the expectation value of the energy in that state is an upper bound to the ground state energy. In the present work, Particle in a box problem is solved by applying variation method & by using MATLAB & MATHCAD software. The wave functions are solved for the ground state & the first excited state. The results obtained are compared with the chosen trial functions of various orders and their combinations. By this one can able to apply the theoretical knowledge and clearly understand the concept of Particle in a box problem. energy Eigen state or ground state, and some excited states. The method consists in choosing a wave depending on one or more parameters, and finding the values of these parameters for which the expectation value of the energy is the lowest possible. The wave function obtained by fixing the parameters to such values is then an approximation to the ground state wave function, and the expectation value of the energy in that state is an upper bound to the ground state energy. Derivation is not always possible to find an analytic solution to the Schrodinger Equation. One can always solve the equation numerically, but this is not necessarily the best way to go; one may not be interested in the detailed Eigen functions, but rather only in the energy levels and the qualitative features of the Eigen functions. And numerical solutions are usually less intuitively understandable. Fortunately, one can show that the values of the energy levels are only mildly sensitive to the deviation of the wave function from its true form, and so the expectation value of the energy for an approximate wave function can be a very good estimate of the corresponding energy Eigen value. By using an approximate wave function that depends on some small set of parameters and minimizing its energy with respect to the parameters, one makes such energy estimates. The technique is called the variation method because of this minimization process. This technique is most effective when trying to determine ground state energies, so it serves as a nice complement to the WKB approximation, which works best when one is interested in relatively highly excited states, ones whose deBroglie wavelength is short compared to the distance scale on which the wavelength" @default.
• W895726340 created "2016-06-24" @default.
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• W895726340 date "2015-04-20" @default.
• W895726340 modified "2023-09-23" @default.
• W895726340 title "Solving Particle in a Box Problem Using Computation Method" @default.
• W895726340 cites W2947596026 @default.
• W895726340 doi "https://doi.org/10.6084/m9.figshare.1385168.v1" @default.
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