Schrodinger wave equation is a mathematical expression describing the energy and position of the electron in space and time, taking into account the matter wave nature of the electron inside an atom.
It is based on three considerations. They are;
- Classical plane wave equation,
- Broglie’s Hypothesis of matter-wave, and
- Conservation of Energy.
Schrodinger equation gives us a detailed account of the form of the wave functions or probability waves that control the motion of some smaller particles. The equation also describes how these waves are influenced by external factors. Moreover, the equation makes use of the energy conservation concept that offers details about the behaviour of an electron that is attached to the nucleus.
Besides, by calculating the Schrödinger equation we obtain Ψ and Ψ2, which helps us determine the quantum numbers as well as the orientations and the shape of orbitals where electrons are found in a molecule or an atom. Time-dependent Schrödinger equation is represented as;
Or,
