The uncertainty principle

The Heisenberg Uncertainty Principle states that a state of system cannot be prepared in which both the position and momentum of a particle can be defined simultaneously to arbitrary accuracy.

$\Delta x \Delta p \ge \frac{\hbar}{2}$

Key Points:

  • It is physically impossible to measure simultaneously the exact position and exact momentum of a particle.
  • The inescapable uncertainties do not arise from imperfections in practical measuring instruments
  • The uncertainties arise from the quantum structure of matter


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