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on the basis of which wave equation schrodinger wave equation is derived?

Physics
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Schrodinger wave equation is like the most basic thing for quantum mechanics and matter waves.. just like how y = asing(wt - kx).. is a basic equation for a travelling wave!
please explain it briefly..i mean the derivation
That the Schrodinger Equation describes the time evolution of the system is a postulate of quantum mechanics. There are some "motivational derivations" using the de Broglie wavelengths and some equations for light but in the end it's one of the postulates of quantum mechanics. A very brief motivation is that the first term is the kinetic energy and the second term is the potential energy.

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Prior to the introduction of QM, Einstein and DeBroglie introduced the wave theory of particles, It is said that an off hand comment was made by Debye that if particles act like wave maybe there is a wave equation that describes them. Schroedinger took this comment seriously and using a formalism developed by W. R. HamIlton in the 1820's, which brought together wave and particle dynamics, developed his wave equation which by the way he had to get the help of a mathematician to solve.
Is this what you were looking for: http://www.nipne.ro/rjp/2011_56_9-10/1053_1056.pdf (the HAMILTON-JACOBI equation)
I wonder why the author of http://www.nipne.ro/rjp/2011_56_9-10/1053_1056.pdf did not reference Schoedinger's original paper .Schrödinger, E. (1926). "Quantisierung als Eigenwertproblem; von Erwin Schrödinger". Annalen der Physik, (Leipzig): 361–377.

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