Erwin Schrodinger, 12 August 1887 – 4 January 1961, is well known for the Schrodinger Equation which he received a Nobel Prize in Physics for in 1933. The Schrodinger Equation is "the wave equation of non relativistic quantum mechanics". He showed, through math, that waves can be used to describe electrons in atoms.
He also built off of Bohr's model of the atom with the Electron Cloud Model. This model depicts the floating motion of the electrons, rather then them having a set path of travel. He determined the probability location of electrons in atoms. According to Schrodinger, electrons stuck in their orbits would set up "standing waves". He said that you could describe only the probability of where an electron could be, it was not definite. The distributions of these probabilities formed areas of space about the nucleus were called orbitals. An orbital is a wave function describing the state of a single electron in an atom.