Register to reply

Commutation of operators

by solas99
Tags: commutation, operators
Share this thread:
solas99
#1
Jan15-12, 03:50 PM
P: 69
what is the physical significance of the commutation of operators?
Phys.Org News Partner Physics news on Phys.org
New approach to form non-equilibrium structures
Nike krypton laser achieves spot in Guinness World Records
Unleashing the power of quantum dot triplets
tom.stoer
#2
Jan15-12, 04:59 PM
Sci Advisor
P: 5,364
One can e.g. derive the Heisenberg uncertainty principle
lpetrich
#3
Jan15-12, 06:15 PM
P: 518
An interpretation of operators' commutator is what happens when those operators' operations interfere with each other. This interference is what leads to the Uncertainty Principle.

Like position and momentum operators. These operators measure those quantities, and attempting to do so for the same direction of position and momentum leads to interference. However, position and momentum in orthogonal directions do not interfere with each other.

jfy4
#4
Jan15-12, 10:58 PM
jfy4's Avatar
P: 647
Commutation of operators

another snazzy way to think about them is as indicators for "curvature". Since it suits a lot of people to think about physics as geometry, the commutation of operators can be used to see the curvature, more or less, of the "space" of states.
ibysaiyan
#5
Jan16-12, 05:23 AM
P: 437
Quote Quote by lpetrich View Post
An interpretation of operators' commutator is what happens when those operators' operations interfere with each other. This interference is what leads to the Uncertainty Principle.

Like position and momentum operators. These operators measure those quantities, and attempting to do so for the same direction of position and momentum leads to interference. However, position and momentum in orthogonal directions do not interfere with each other.
So basically we can infer either of the two quantities due to the commutative nature of the operators.Provided, they happen in the same direction , am I right to think it this way ?


Register to reply

Related Discussions
Commutation relation of operators Quantum Physics 2
Commutation of operators in QM Advanced Physics Homework 1
Raising and lowering operators & commutation Advanced Physics Homework 7
Commutation of angular momentum operators Advanced Physics Homework 1
Commutation of 2 operators using braket notation? Advanced Physics Homework 5