Linked Questions

130 votes
8 answers
38k views

What is $\Delta t$ in the time-energy uncertainty principle?

In non-relativistic QM, the $\Delta E$ in the time-energy uncertainty principle is the limiting standard deviation of the set of energy measurements of $n$ identically prepared systems as $n$ goes to ...
Hobo's user avatar
  • 1,325
58 votes
14 answers
8k views

Why is it impossible to measure position and momentum at the same time with arbitrary precision?

I'm aware of the uncertainty principle that doesn't allow $\Delta x$ and $\Delta p$ to be both arbitrarily close to zero. I understand this by looking at the wave function and seeing that if one is ...
catmousedog's user avatar
23 votes
11 answers
7k views

What does Heisenberg's uncertainty principle tell about nature? [closed]

I agree with the fact that the principle points out to the inaccuracy in the measurement of the two quantities of the particles (momentum and position). But measurements apart, does it explain ...
Swaroop Joshi's user avatar
17 votes
5 answers
2k views

How can I accurately state the uncertainty principle?

In almost every introductory course, it is taught that the uncertainty principle happens due to disturbance in the system to be measured. Teachers give these examples that induce students to ...
1__'s user avatar
  • 1,604
9 votes
2 answers
805 views

Do quantum measurements violate conservation laws?

When we measure the spin angular momentum of a particle in an axis different to its current spin, we change the direction of its spin, which taken by itself would be a violation of the law of ...
zucculent's user avatar
  • 1,405
4 votes
3 answers
1k views

Physical interpretation of Uncertainty

Uncertainty of an operator $\hat{A}$ when observing a state $|\psi\rangle$ is defined as \begin{equation} \Delta A_{\psi} = |(\hat{A} - \langle\hat{A}\rangle)\psi| \end{equation} Now assume that there ...
QuantumOscillator's user avatar
5 votes
2 answers
593 views

Uncertainty principle: for an individual particle?

In some textbooks about quantum mechanics, the position-momentum uncertainty principle is treated as being valid for an individual "particle", with $\Delta x\cdot\Delta p\geq\hbar/2$ ...
gamma1954's user avatar
  • 1,169
4 votes
2 answers
1k views

What happens to Pauli's argument (that says that there is no time operator) when applied to $X$ operator for some simple systems?

An argument by Pauli is usually referred to in the literature when it is stated that there cannot be a time operator in quantum mechanics. This argument can be found as a footnote to P63 of W. Pauli, ...
Curiosa's user avatar
  • 427
3 votes
1 answer
605 views

What is an ensemble of particles in quantum mechanics?

According to Griffith's Introduction to Quantum mechanics in section 1.5 Momentum, he said that " the expectation value is the average of repeated measurements on an ensemble of identically ...
My Essential Learning's user avatar
-5 votes
2 answers
295 views

A problem with the uncertainty principle [closed]

It is postulated that the particle is described by a state vector $\Phi$, which is an element of Hilbert space. Let's suppose that there are two Hermitian operators $A$ and $B$, representing two ...
wawa's user avatar
  • 77
0 votes
2 answers
596 views

Is there any difference between expectation value and average value in quantum mechanics?

Is there any difference between expectation value and average value in quantum mechanics? If there is no difference then why give them different names?
QM_Search's user avatar
-4 votes
4 answers
156 views

What is the evidence for the claim that the Uncertainty Principle is not a result of inadequacies in the measuring instruments/technique? [closed]

If we accept that quantum mechanics is a good theory for describing microscopic systems (for, there is plenty of evidence that suggests quantum mechanics is a good theory), then the property of non-...
Pavel Borisov's user avatar