Different versions of the uncertainty principle

[touqra]

I have seen different versions of the uncertainty principle. Which is the correct one?

$$\Delta x \Delta p >= h$$

$$\Delta x \Delta p >= \frac{\hbar}{2}$$

 

[Bright]

Second one is correct.

 

[denian]

I understand that the uncertainty principle is a fundamental concept in quantum mechanics that states that it is impossible to simultaneously know the exact position and momentum of a particle. Therefore, it is not a matter of one version being more correct than the other, but rather, they are different formulations of the same principle.

Both versions of the uncertainty principle, \Delta x \Delta p >= h and \Delta x \Delta p >= \frac{\hbar}{2}, have been derived and shown to be valid in different contexts. The first version, where h is the Planck constant, was originally proposed by Werner Heisenberg in 1927. However, later developments in quantum mechanics led to the introduction of the reduced Planck constant, \hbar = \frac{h}{2\pi}, resulting in the second version of the uncertainty principle.

Furthermore, the uncertainty principle is not a fixed mathematical equation, but rather a concept that is applied in various forms to different physical systems. For example, in the case of energy and time, the uncertainty principle is expressed as \Delta E \Delta t >= \frac{\hbar}{2}. This shows that the uncertainty principle is a fundamental principle that applies to various physical quantities and can be expressed in different forms.

In conclusion, both versions of the uncertainty principle are valid and reflect the same fundamental concept. As scientists, it is important to understand the different formulations and apply them appropriately in our research and experiments.