Final answer:
The modern quantum mechanical model of the atom comes from the solution to Erwin Schrödinger's equation, which accurately describes the behavior of electrons based on wave functions.
Step-by-step explanation:
The modern quantum mechanical model of the atom comes from the solution to Erwin Schrödinger's equation. Schrödinger, an Austrian physicist, used the wave-particle duality of the electron to develop and solve a complex mathematical equation that accurately described the behavior of the electron in a hydrogen atom. This quantum mechanical model is a radical departure from the previous Bohr model and is based on the idea of wave functions, which give the probability of finding an electron at a given point around the nucleus.