Question

What is the meaning of Delta in the formula
dx*dp>=h/2pi. Why will quantum effect occurs in a larger scale if Planck's constant is larger?
In my understanding, delta means the rate of change of x or p, and if one is really small(precise), another will become really large(uncertain), but why there should be a ">="?

Answer 1

I see you're talking about the uncertainty principle \[\Delta p \Delta x \ge \frac{ h }{ 2 }\]
This is the relations between simultaneous measurement of momentum in the x - direction with precision \[\Delta x\] for a particle. They must always be \[\ge \] because it tells us at a certain point where the particles will be exactly, and at a certain point there will be a limit that "breaks" the relationship. So if you try to measure x with infinite precision, the uncertainty in p increases.

Answer 2

It's not very intuitive, so these videos might help you understand: https://www.youtube.com/watch?v=7vc-Uvp3vwg
https://www.youtube.com/watch?v=0FGo8mi-5w4
There are many videos online that will help you, and looking at the experiments is kind of cool, and will help you understand it more :).

Answer 3

Heisenberg's uncertainty principal is NOT a statement about measurement.

Answer 4

The \(\Delta\), is the uncertainty (range),
i.e. \(x=x\pm\Delta x\)

Answer 5

The greater than or equal sign is a mathematical consequence of the theory of linear operators on Hilbert Spaces. It matches our intuition since the multiplication of the uncertainties can be much larger depending on how careful we are when making measurements. Non the less, due to the quantum nature of... well nature, no experiment has been able to get the multiplication of the uncertainties less than \(\frac{ h }{ 2 \pi }\)

Answer 6

As stated previously:
"Heisenberg's uncertainty principal is NOT a statement about measurement."
Similarly, it is NOT related to experimental uncertainty.