What is Heisenberg Uncertainty Formula?

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Discussion Overview

The discussion centers on the Heisenberg Uncertainty Principle Formula, exploring its definitions and variations. Participants reference different formulations and clarify the distinction between constants involved in the principle.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant presents a version of the formula as Δx(Δmv) ~ h/2∏ and ΔxΔp ~ (h-bar).
  • Another participant asserts that the "correct" version is ΔxΔp ≥ (h-bar)/2, emphasizing that the deltas represent statistical standard deviations.
  • Some participants note that simplified versions of the formula exist, which may differ by numerical factors for less rigorous applications.
  • A participant highlights the distinction between Planck's constant (h) and reduced Planck's constant (h-bar = h/2∏).

Areas of Agreement / Disagreement

Participants express differing views on the formulation of the Heisenberg Uncertainty Principle, with no consensus on a single "correct" version. The discussion includes both rigorous and simplified interpretations.

Contextual Notes

The discussion includes assumptions about the definitions of statistical terms and the context in which different formulations are used, which remain unresolved.

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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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