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A new series solution associated with the quantum harmonic oscillator

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dc.contributor.author Umul, Yusuf Ziya
dc.date.accessioned 2022-03-01T11:58:34Z
dc.date.available 2022-03-01T11:58:34Z
dc.date.issued 2021-11
dc.identifier.citation Umul, Yusuf Ziya (2021). "A new series solution associated with the quantum harmonic oscillator", Optik, Vol. 25. tr_TR
dc.identifier.uri http://hdl.handle.net/20.500.12416/5057
dc.description.abstract In the non-relativistic case, the problem of quantum harmonic oscillator is solved by the aid of the Schro spacing diaeresis dinger equation. An additional term of potential energy that is related with the square of the spatial coordinate is also included in the equation. A second order linear differential equation is obtained in the stationary state. The direct solution gives the wave function in terms of the parabolic cylinder functions. This solution leads to the Hermite polynomials when the quantization of energy is considered. However, the derived expression of the wave function does not yield the correct functions for the limiting case, in which the potential energy is zero. We put forth an alternative solution for the second order linear differential equation. First of all, a new series expression is suggested as an ansatz for the power series solution of differential equations. The coefficients of the series are obtained in terms of recurrence relations. Some computational simulations are given. tr_TR
dc.language.iso eng tr_TR
dc.relation.isversionof 10.1016/j.ijleo.2021.167704 tr_TR
dc.rights info:eu-repo/semantics/closedAccess tr_TR
dc.subject Quantum Harmonic Oscillator tr_TR
dc.subject Schrödinger Equation tr_TR
dc.subject Differential Equations tr_TR
dc.title A new series solution associated with the quantum harmonic oscillator tr_TR
dc.type article tr_TR
dc.relation.journal Optik tr_TR
dc.contributor.authorID 42699 tr_TR
dc.identifier.volume 25 tr_TR
dc.contributor.department Çankaya Üniversitesi, Mühendislik Fakültesi, Elektronik ve Haberleşme Mühendisliği Bölümü tr_TR


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