Uncertainty principle

Explanation

The uncertainty principle states that every particle has a wave nature associated with it and it is impossible to know both the position and momentum of the wave beyond a certain level of precision at the same time. This is because the particle exists in a superposition of position and momentum, and if you were to know the position of the particle with high precision, then the momentum cannot be precisely known fundamentally. This principle is mathematically expressed as follows.

[math]\sigma_{x}\sigma_{p} \geq \frac{\hbar}{2}[/math]

This explains that the products of standard deviations of the position [math]\sigma_{x}[/math] and momentum [math]\sigma_{p}[/math] cannot be small at the same time. If the standard deviation of position is small, then it is apparent that the position of the particle is known with high precision. And by the fundamental nature of the particles, the standard deviation of the momentum should now be higher enough that the product of the two should be greater than [math]\frac{\hbar}{2}[/math], where [math]\hbar[/math] is the reduced Planck's constant.