Final answer:
Option (D): Erwin Schrödinger developed the Schrödinger equation in 1926, which accurately explains the quantum nature of the electron in an atom.
Step-by-step explanation:
The scientist who developed a complex equation to accurately explain the quantum nature of the electron in an atom is Erwin Schrödinger. Schrödinger formulated the Schrödinger equation in 1926, using the wave-particle duality concept. This equation is central to the quantum mechanical model of the atom and describes electrons as three-dimensional wavefunctions, with the modulus squared of the wavefunction representing the probability density of finding an electron at a particular location.