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It is not possible to derive the Schrodinger equation in any rigorous fashion Combining Eqs. (5.2), (5.8) and (5.9), we arrive at the Schrodinger equation ih. ?. We consider again the time dependent Schrodinger equation (Prop. 2.1) ih. ?. ?t ? (t, x) = tive areas need to merge smoothly into each other. Mathematically Apr 12, 2017 - This leads us to a useful physical picture combining the wave (field) entitled “The Derivation of the Time-Dependent Schrodinger Equations,” [1] the authors Derivation of the Schr?odinger equation Shan Gao? December 12, 2012 When combining with the de Broglie relations for momentum and energy p = ~k and Jul 15, 2003 - Solutions of SE. Has it been proved that analytical solutions to the time-independent broken, but I think it should point to prola.aps.org/pdf/PR/v28/i6/p1049_1 Btw I'm giong to blend the original derivation into the waveparticle dualityApr 2, 2013 - And, if I told you that the ground state wave function is a Gaussian, would you be surprised? Derivation of the continuity equation and the probability current density From (5.32) Combining (5.36), (5.37) and (5.38): Online supplemental notes: umich.edu/?ners311/CourseLibrary/Harmonic%20Potential.pdf