Erwin Schrodinger was a physicist from Austria who did most of his work in the early to mid 1900's. His "experiments" to come up with his model were math related and he is well known for his wave equation. He thought of electrons as waves and he applied the Uncertainty Principle to his model by saying that electrons had specific orbitals (like in Bohr's model), but the position is based on probability, so it doesn't try to tell you where an electron is, it tells you where it might be.

The big dot in the center is the nucleus and the little dots surrounding it is where the electrons have been. Imagine that the electron has left a trace wherever it has been.

Instead of specific planet-like orbits, the orbits are pictured as smeared clouds.

Schrodinger combined the ideas of previous scientists with his own ideas to come up with this model. It has electrons (discovered by J.J. Thomson), protons (discovered by Eugene Goldstein), a nucleus (discovered by Ernest Rutherford), and the idea of Quantum Mechanics developed by Max Planck. All of this is combined with his "wave" theory and the Uncertainty Principle (developed by Heisenberg). To this day, nothing about Schrodinger's model has been proven wrong and it is thought to be accurate.