The Original Derivation of Schrödinger Equation

Taken from wikipedia:

In January 1926, Schrödinger published in Annalen der Physik the paper "Quantisierung als Eigenwertproblem" [tr. Quantization as an Eigenvalue Problem] on wave mechanics and what is now known as the Schrödinger equation. In this paper he gave a "derivation" of the wave equation for time independent systems, and showed that it gave the correct energy eigenvalues for the hydrogen-like atom. This paper has been universally celebrated as one of the most important achievements of the twentieth century, and created a revolution in quantum mechanics, and indeed of all physics and chemistry.

A second paper was submitted just four weeks later that solved the quantum harmonic oscillator, the rigid rotor and the diatomic molecule, and gives a new derivation of the Schrödinger equation.

A third paper in May showed the equivalence of his approach to that of Heisenberg and gave the treatment of the Stark effect.

A fourth paper in this most remarkable series showed how to treat problems in which the system changes with time, as in scattering problems. These papers were the central achievement of his career and were at once recognized as having great significance by the physics community.

The English translation of these papers could be downloaded HERE.