(s) State the Heisenberg Uncertainty Principle. (b) The product of the uncertainties in Heisenberg Uncertainty Principle is equal to or greater than a const...
Question 1 Report
(s) State the Heisenberg Uncertainty Principle.
(b) The product of the uncertainties in Heisenberg Uncertainty Principle is equal to or greater than a constant. State the mathematical expression for this constant.
Answer Details
(a) Heisenberg Uncertainty Principle
It is impossible to determine simultaneously and with perfect accuracy both the position and the momentum of a particle. The more precisely the position is known, the less precisely the momentum can be known, and vice versa.
(b) Mathematical expression
The product of the uncertainty in position \(\Delta x\) and the uncertainty in momentum \(\Delta p\) satisfies
\[ \Delta x \,\Delta p \;\geq\; \frac{h}{4\pi} \]so the constant is \(\dfrac{h}{4\pi}\), where \(h\) is Planck's constant. (Equivalently \(\dfrac{\hbar}{2}\).)
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