**What is the** **Free particle Wave equation? Derive Energy and momentum operator with the help of Free particle Wave equation**

**Answer:**

**Free particle Wave equation:**

If we assume that matter waves are produced due to variation in the wave function in a similar manner as sound waves are produced due to variation in pressure and electromagnetic waves are produced due to variation in electric and magnetic fields. The *wave function* is a function of both the position and time. Now, let us assume that wave function for the wave moving along positive *x* direction can be represented as

## This is the free particle wave equation.

**Energy and momentum operator:**

**Energy and momentum operator:**

On partially differentiating with respect to *t* to equation (3), we get