What is Heisenberg Uncertainty Formula?

[ZedCar]

What is the Heisenberg Uncertainty Principle Formula?

Here:
http://www.people.vcu.edu/~rgowdy/mod/122/xmp4.htm

It is quoted as Δx(Δmv) ~ h/2∏
which is ΔxΔp ~ (h-bar)

Here:
https://en.wikipedia.org/wiki/Uncertainty_principle

It is quoted as ΔxΔp ~ (h-bar)/2

 

[jtbell]

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.

 

[ZedCar]

Thank you for that.

 

[Studiot]

Please note the difference between h (Planck's constant) and hbar = h/2∏ (reduced Planck's constant).

Google will find plenty.

 

[pmacias]

The Heisenberg Uncertainty Principle is a fundamental principle in quantum mechanics that states that it is impossible to simultaneously know the exact position and momentum of a particle with absolute certainty. The Heisenberg Uncertainty Formula, also known as the Heisenberg Uncertainty Principle Formula, mathematically represents this principle by describing the relationship between the uncertainty in position (Δx) and the uncertainty in momentum (Δp) of a particle. The formula, written as ΔxΔp ~ (h-bar)/2, shows that the product of these two uncertainties is equal to or greater than a constant value, h-bar, which is Planck's constant divided by 2π. This means that the more precisely we know the position of a particle, the less we know about its momentum and vice versa. The Heisenberg Uncertainty Principle has significant implications in quantum mechanics and has been verified through numerous experiments.