observables Definition and 112 Threads

Homework Statement If A and B were observables, and say the simultaneous eigenkets of A and B {|a',b'>} form a complete orthonormal set of base ket. Can we conclude that [A,B]=0? 2. The attempt at a solution Assume {|a',b'>} is incompatible: AB|a',b'>=a'b'|a',b'> <-- skipped several steps...

I've posted similar questions on a different forum previously, but since I'm feeling a bit guilty about going on at the one person there who answers, I'll post these here. Hope it's ok if I don't follow the template since they're more conceptual than a standard problem. Any help appreciated...

Is ``OBSERVABLES'' a word? I know ``OBSERVABLE'' (singular is), but what about the plural?

Hi, In Weinberg's QFT book(section 2.2), he said after proved the generator of the symmetry group is Hermitian and can be a candidate for an observable: My questions: 1. Does the observable here mean at least in principle, we can measure it in experment? 2. Does generator of any symmetry...

could someone explain this paragraph taken from "concepts of modern physics" by arthur beiser pg175? I'm having trouble understanding it... "A dynamical variable G may not be quantized. In this case, measurements of G made on a number of identical systems will not yield a unique result but...

Hi, I've had a question ever since my quantum classes that's pretty simple I guess, but still seems to elude me. So here it is: One text I used for quantum (Liboff's "Introductory Quantum Mechanics") says that in classical mechanics, there is a "vector of the state" of a system, that...

In the context of observables in QM the rate of change of the In the contest of observables in QM the rate of change of the expectation value of an observable A is defined by: d<A>/dt= d< Y | A Y>/dt = < d Y/dt | A Y > + < Y | dA/dt . Y > + < Y | A dY/dt> My question is about the second...

I have trouble understanding operators and observables: Does <A> the average value of an observable and the variance depend on the state of the system? What does it have to do with the Hamiltonian? Thanks!

The question is: Prove that, for a 1-D harmonic oscillator, every conserved observable is a function of the energy. Find, for the 3-D harmonic oscillator, some conserved observable not a function of the energy and angular momentum. My first problem with this question is I'm not sure what...

An observable in QM is to be represented by a self-adjoint/hermitean operator, so that the eigenvalues are real numbers. I could not find the answer to : are all self-adjoint/hermitean operators actually observables ? Thank you for any help !

Incompatible observables do not share a complete set of common eigenfunctions, because their operators do not commute. It seems that, incompatible observables like x and p_x, S_x and S_y do not have any common eigenfunction at all. Can anyone give a concrete example of a pair of...

I understand that observables in quantum mechanics are represented by hermitian operators, which are converted into a matrix when expressed in a particular basis. I also understand that when the basis used is an eigenbasis of the operator, the matrix becomes diagonal, having the eigenvalues as...