Dear Aspirant

I hope you are doing well

Matter waves are defined as waves associated with a moving quantum particle.
Wave is formed by matter or in simple words particles. Every matter made by particles have wave like properties which mean it can behave as both particle and wave.
The wavelength of matter wave is called "de-Broglie Wavelength"

Mathematically,In Phase means that thephaseangle of twowavesare the same, or are in arithematic progression, with the common difference being (2 x pi), whileOut of Phase makes the difference in the twophaseangle to be 180 degrees, or (2n x pi ) + 180 degrees.

( pi = 3.141)

I hope it will help you

Thank you