 # Schrodinger Wave Equation Simplified

## Schrödinger Wave Equation Schrödinger equation

The behavior of sub-atomic particles can’t be explained by classical mechanics based on Newton’s laws of motion and thus came a new theory that explained the anomalies in subatomic particles. The theory is quantum mechanics. It was developed in early 20th century by Erwin Schrödinger and Werner Heisenberg independently. However, the notion of quantum mechanics, based on the ideas of wave motion is a result of Schrödinger wave equation developed by Schrödinger. This equation is called as the fundamental equation of quantum physics and it won the scientist a Nobel Prize in physics in 1933.

It is a partial differential equation which incorporated wave-particle duality of matter and the total energy associated with them. This function describes how the wave function of a physical system evolves with time and describes the probability of finding an electron. It can be simplified for a system such as an atom or a molecule whose energy does not change with time. For them, the Schrödinger equation is written as

Hψ = Eψ

Where H is a mathematical operator called Hamiltonian.

The solutions of this equation are quantum mechanical systems and are collectively known as Schrödinger Picture. The solution provides:

1. Possible energy levels an electron can occupy

This leads to the formation of concepts of quantized shells, subshells, and orbitals. An electron can occupy shells, subshells, and orbitals of different energy.

1. The wavefunction of electron associated with each energy shell

The wave function of electron tells about the shape and size of orbital viz. the shape of s, p, d and f orbitals.

These quantized energy states and corresponding wave function are characterized by three quantum numbers:

1. Principle quantum number (n): This tells about the shell in which an electron can be found. (K, L, M, N)
2. Azimuthal quantum number (l): This tells about the subshell in which electron can be found (s, p, d, f )
3. Magnetic quantum number (m): This tells about the orbitals in which electron can be found. (As for P it can be Px , Py or Pz)