Atomic orbitals are the quantum states of the individual electrons in the electron cloud around a single atom. The three-dimensional region where the probability of finding an electron is maximum around the nucleus. Each sub-shell contains a various number of orbitals.
Example: s-sub shell contains 1 orbital, p-sub shell contains 3 orbitals, d-sub shell contains 5 orbitals, and f-sub shell contains 7 orbitals.
The Schrodinger equation is a linear partial differential equation that describes the wave function or state function of a quantum-mechanical system.