BiGyElLoWhAt said:There's quite a few versions of Heisenberg's Uncertainty Principle. ##\Delta x \Delta p \geq h \ \text{or}\ \geq \hbar \ \text{or}\ \geq \frac{\hbar}{2} ## are the main 3 that I'm aware of, at least for position momentum uncertainty. The last reported (most accurate) that I remember was hbar over 2, but they may use a different version, depending on how old the documents are.
I also don't see where you're talking about. I just skimmed through the solutions, but everywhere that I noticed them speaking of uncertainty they either used ##\delta x \ \text{&}\ \delta p \ \text{or} \ \Delta x \ \text{&}\ \Delta p ##
Which problem are you referring to?
Edit** Somehow I missed 2.iv -.-
They're not talking about uncertainty. They're talking about the total energy of the ground state. The ground state should never be lower than 1 quantum.
So I believe that the measured values of x and p in the ground state should be of the order of the uncertainty principle. There may be more to the story, if so, someone else would have to jump in and inform us. I'm not a huge quantum guy.
Heisenberg's Uncertainty Principle states that it is impossible to know the exact position and momentum of a particle at the same time. In other words, the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa.
German physicist Werner Heisenberg is credited with discovering the Uncertainty Principle in 1927.
Heisenberg's Uncertainty Principle is significant because it sets a fundamental limit on the precision with which we can measure particles at the subatomic level. It also challenges the classical notion of determinism and highlights the inherently probabilistic nature of the quantum world.
In everyday life, Heisenberg's Uncertainty Principle has very little impact. It only becomes significant at the subatomic level, where the laws of classical physics no longer apply. However, technologies such as electron microscopes and MRI machines rely on the principles of quantum mechanics and the Uncertainty Principle to function.
The observer effect is the idea that the act of observing or measuring a particle changes its behavior. This is closely related to Heisenberg's Uncertainty Principle because the very act of measuring a particle's position or momentum affects its behavior and introduces uncertainty into the measurement.