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|Uncertainty Principle||I 39
Uncertainty Relation/Feynman: Question: why do the negative charges (electrons) not simply sit on the positive ones, given that they are drawn to each other? Why do they not come close enough to each other to compensate themselves? Why are the atoms so large?
Uncertainty Relation: if the electrons were in the nucleus, we would know their position exactly. Then the uncertainty relation would require them to have a very large (but uncertain) impulse, i.e. very high kinetic energy. With this energy they could tear themselves from the core.
They make a compromise and "tremble" in a minimal movement.
Indetermination Principle/Uncertainty Relation/Feynman:
We can specify a probability density p1(x) such that p1(x) Δx is the probability that the particle is located between x and x + Δx.
Fig. I 99 Scanner: two bell curves, p2(v) against p1(x = displaced).
Probability density p2(v).
The probability of the velocity being between v and v + Δv is p2(v)Δv.
Quantum mechanics: the two functions p1(x) and p2(v) cannot be selected independently of each other.
Thus nature requires that the product of the two widths is at least equal to the number h/m. m = particle mass h: Planck's quantum of action.
[[Δx] x [Δv] ›= h/m.
The right side is a constant!
E.g. hydrogen atom: the uncertainty for the location of the electron is as big as the total atom!
Indeterminacy Principle/Quantum Mechanics/Feynman: the whole quantum mechanics is based on the correctness of the uncertainty relation.
Uncertainty Principle/HeisenbergFeynman: originally: if measurements are carried out at any object, and the x component of its momentum can be determined with an indeterminacy Δp, then its x coordinate cannot be detected more precisely than Δx = h/Δp.
The product of the uncertainties of the position and momentum of a particle must always be greater than Planck's constant. (Special case).
General form: to decide which of two alternatives is selected it is
impossible to develop a device which does not simultaneously destroy the interference pattern.
Experiment: we can show that the UR must be true: For example, a double gap with a moving wall.
When the vertical component of the electron pulse has changed, the plate must return in the opposite direction with the same momentum. Then the electron passes through the other gap.
Important Point: this allows us to say through which gap the electron passed! But we should then know the scale of the impulse of the screen before the electron passes through. It is possible afterwards, but not at the same time. We cannot say exactly where the gaps are in the moving plates example.
The fluctuations of the interference pattern will be blurred. >No interference.
Vom Wesen physikalischer Gesetze München 1993
Vorlesungen über Physik I München 2001