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i mean Bohr's model and Schroedinger equation are based on simple mathematics so why couldn't Einstein or another mathematician to discover them ?

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closed as primarily opinion-based by Conifold, J. W. Perry, Geremia, David Hammen, Logan M Aug 20 '16 at 23:39

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Because he was too busy discovering general relativity at the time. $\endgroup$ – Conifold Aug 20 '16 at 17:32
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    $\begingroup$ If Einstein was a genious, why didn't he invent spell-checkers? $\endgroup$ – Ben Crowell Aug 20 '16 at 23:57
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First came the Rutherford model (1911), based on the Rutherford scattering experiments (1909) and the discovery of the nucleus. The Rutherford model had several defects, but most importantly, how were the electrons kept in orbit about the nucleus, whose positive charge was constantly drawing them in? Maxwell's equations require that an accelerating charge must radiate energy, and so the orbits couldn't be stable.

Neils Bohr (1912) came to work with Rutherford; he analyzed the defects of the model, and applied Planck's quantum of energy (1900) to the problem.

The result, after much careful pondering of the situation, including the experimental results, was the Bohr model (1913).

This model works quite well for the hydrogen atom, but was soon shown to have its own defects. These were resolved, in part, by de Broglie's quantum waves (1924).

Putting together the Planck relation, $E=hf$ with the de Broglie relation (in wave mechanics form), $P=hk$, one can write the equation for a plane wave, here to be interpreted as de Broglie's matter wave, as $\psi = exp(i(kx-ft))=exp(i/h(px-Et))$.

This "wave equation" was then solved by Schrodinger (1925) by applying Hamiltonian mechanics to the problem. Here the Hamiltonian is not the expression for the energy, but instead is the operator which extracts the energy from the wave function. This is not the place to go into all the details of how he came to his solution, but he was in part inspired by Heisenberg's slightly earlier results, as well as the de Broglie wave. The two methods are complementary.

Note that Bohr's reputation is not based solely upon his erroneous atomic model. If Einstein had taken an interest in Rutherford's results, and had put aside his work on gravitation for half a year, he may have come up with something similar - but probably would not have published for the model only works for Hydrogen. Why would a successful scientist want to publish something that is obviously wrong from the beginning?

By 1924, Einstein was already past his prime, and had completed major works on statistical mechanics, special relativity, general relativity, as well as several works on condensed matter; his most recent work was on light (1916) and Bose-Einstein statistics (1924). He had made major contributions to the "old quantum theory", and simply missed the boat as it sailed by.

After all, one cannot do everything, and even if the equations look simple to you, there are many subtle issues underlying their development.

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