de Broglie’s Hypothesis

Light is a wave or particle debate was going on for centuries and eventually we all came to know it behaves both. Sometime light has wave properties and sometime light has particle properties. It is like humans. Behaves differently with out using a well known rationale.

de Broglie brought an insight that the both wave & particle properties applies to matter and also the wave length of the matter inversely proportional to momentum.

The above relationship between the momentum and wavelength is given below.

The wave length is equal to the ratio of Plank’s constant and momentum.

Wave Number:
It is equivalent of frequency in the spatial domain. It is a measure of unit of repeating waves per unit of space.

I was not specific in the video. The angular wave number or circular wave number is denoted by k and is given by

The presenting the Plank’s constant in angular form is given by

Using the above equations in de Brogile’s equation representing the relationship between wavelength and momentum we get

Wave Function:
The wave function is the crux of the Schrodinger equation. The plane wave is taken as the wave function.