Skip to main content
3 votes
Accepted

Problem Deriving "The General Uncertainty Principle" in Section 5.7 of Susskind's "Quantum Mechanics"

You are correct, but there's one last simplifying step. The norm of the product is the product of the norms. For two complex numbers, $z_1$ and $z_2$: \begin{equation} |z_1\cdot z_2| = |z_1|\cdot|z_2| ...
Aiden's user avatar
  • 1,753
2 votes
Accepted

For any pure state, can I find a pair of non-commuting observables which saturate the uncertainty bound?

The answer is yes, to both questions. For the first we can choose \begin{align} A = |\psi\rangle\langle\psi|, \end{align} and let $B$ be anything we like and it'll saturate the bound (because the ...
ors's user avatar
  • 409
1 vote

How does wave function collapse relate to uncertainty in position when measurement intervals approach zero?

In quantum mechanics, measuring the position of a particle causes the wave function to collapse, fixing the particle at a measured position. No it doesn't. The equations of motion of quantum systems ...
alanf's user avatar
  • 8,338
1 vote
Accepted

How does wave function collapse relate to uncertainty in position when measurement intervals approach zero?

From Griffiths' Introduction to Quantum Mechanics: The expectation value is the average of measurements on an ensemble of identically-prepared systems, not the average of repeated measurements on one ...
Vincent Thacker's user avatar
1 vote

Can the measurement problem be overcome?

There are actually a number of problems, or different aspects of the measurement problem: Certain combinations of observables, like position and momentum, cannot be independently measured. Measuring ...
Jos Bergervoet's user avatar
1 vote

Can the measurement problem be overcome?

However in most cases where measurement affects a system we can account for the perturbation. Why is this not possible in quantum mechanics(perhaps even statistically)? And has there been any ...
alanf's user avatar
  • 8,338
1 vote

Can the measurement problem be overcome?

In science, "why" is often quite an unsatisfying question. Science is not focused on the "why" as much as predicting behaviors. Why those behaviors happen is a philosophical ...
Cort Ammon's user avatar
  • 49.9k
1 vote

What happens to the uncertainty principle when I have a particle contained within an inelastic box?

It's impossible to design a box that will continually lower the energy of a trapped particle. This is because a particle in a box has a lowest energy state (the ground state). The energy of the ...
Astute Reader's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible