At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
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.
Not the answer you are looking for? Search for more explanations.
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.