**SchrÃ¶dinger Wave Equation**

The behavior of sub-atomic particles canâ€™t be explained by classical mechanics based on Newtonâ€™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 20^{th} century by Erwin SchrÃ¶dinger and Werner Heisenberg independently. However, the notion of quantum mechanics, based on the ideas of wave motion is a result of SchrÃ¶dinger wave equation developed by SchrÃ¶dinger. 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 SchrÃ¶dinger equation is written as

**HÏˆ = EÏˆ**

Where H is a mathematical operator called Hamiltonian.

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

**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.

**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:

- Principle quantum number (n): This tells about the shell in which an electron can be found. (K, L, M, N)
- Azimuthal quantum number (l): This tells about the subshell in which electron can be found (s, p, d, f )
- Magnetic quantum number (m): This tells about the orbitals in which electron can be found. (As for P it can be P
_{x}, P_{y}or P_{z})

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