Answer to Question #90658 in Quantum Mechanics for Vasiliy

Question #90658
What is Heisenberg uncertainty principle, and how does it work for position and momentum measurements?
1
Expert's answer
2019-06-11T10:01:25-0400

Heisenberg uncertainty principle states that for two non-commuting operators, A and B,


σAσB12<[A,B]>\sigma_A \sigma_B \ge \frac{1}{2}\left\lt[A,B]\right\gt

where

σA=<A2><A>2standard deviation\sigma_A = \sqrt{\left\lt A^2\right\gt-\left\lt A\right\gt ^2} -standard\space deviation

For momentum and position:


σpσx12[p,x]=2\sigma_p \sigma_x \ge \frac{1}{2}[p,x]=\frac{\hbar}{2}

that means that we cannot measure momentum and position with an infinity precision simultaneously.


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