**Branch :**Computer Science and Engineering

**Subject :**Math -2

## Heisenberg's Inequaity

**Heisenberg's Inequality:**

This is the Basic **Heiseberg's Inequality Theorem**:

is called the Dispersion about the point x = a of f. The reasioning behind the definition is that if f (x) is concentrated near x = a, then Δ_{a} f is smaller than when f is not close to zero far from x = a.

**Example: **Consider the charectristic functions:

Which has Fourier Transform

Notice that x_{b} is concentrated near x = 0 for small b. The dispersion about the origin is

and it clear that the dispersion increases as b increases. Notice that the Fourier transform x_{b}^ does not have a finite dispersion about the origin.

The Following results shows that there is a type of inverse relationship between the dispersion of a function and that of its Fourier Transform.