Question

what is uncertainty principle

Answer 1

Question 37352

Since in quantum mechanics, linear momentum and position do not commute ( $[x, p_x] = i\hbar$ ), it is not possible to measure the same component of momentum and position of a quantum object at the same time. Hence, while measuring momentum and position, there is an uncertainty of measurement.

According to Heisenberg uncertainty principle, this uncertainty is $\Delta x\Delta p_x\geq \frac{\hbar}{2}$ , or in terms of energy $\Delta E\Delta t\geq \frac{\hbar}{2}$ . These relations might be derived by different ways in wave mechanics or in matrix mechanics. Sometimes, one might accept this principle as a postulate of quantum mechanics.

In wave mechanics formulation, it is possible to find the "minimizing wave packet" - the wave packet, which minimizes uncertainty (for which $\Delta x\Delta p_{x} = \hbar$ ). It is quite easy to show that this packet is a Gaussian function.