What is Heisenberg Uncertainty Formula?

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The Heisenberg Uncertainty Principle Formula states that the product of the uncertainties in position (Δx) and momentum (Δp) is bounded by the reduced Planck's constant (h-bar), expressed as ΔxΔp ≥ h-bar/2. This principle highlights the inherent limitations in measuring both position and momentum simultaneously with arbitrary precision. While simplified versions of the formula exist, they often omit important numerical factors and are used for rough estimates rather than rigorous calculations. It is crucial to differentiate between Planck's constant (h) and the reduced Planck's constant (h-bar). Understanding these distinctions is essential for accurate discussions of quantum mechanics.
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The "correct" version is

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

It assumes that the "deltas" are defined as the usual statistical standard deviation.

People often use simplified versions that differ by small numerical factors, when they're not concerned with being rigorous, but simply want an order-of-magnitude type statement.
 
Thank you for that.
 
Please note the difference between h (Planck's constant) and hbar = h/2∏ (reduced Planck's constant).

Google will find plenty.
 
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