Go Back   Physics Help Forum > College/University Physics Help > Quantum Physics

Quantum Physics Quantum Physics Help Forum

Reply
 
LinkBack Thread Tools Display Modes
Old Sep 8th 2016, 08:00 PM   #1
Junior Member
 
Join Date: Jul 2016
Posts: 7
Understanding the Uncertainty principle

Hi everybody,
I was reading about the Uncertainty principle and I came across the statement: "the position-space wavefunction of a minimum-uncertainty state is a Gaussian. Indeed, because it’s a minimum-uncertainty state, its momentum-space wavefunction is also a Gaussian." Unfortunately it was stated without any mathematical proof or diagrams so I am a bit puzzled!
Also, what does it mean exactly that: "The first energy level of a system is minimum uncertainty." My guess it that it means for lower energies the uncertainty in the energy is minimum. However, due to the quantized nature of the energy levels, how is it possible to be uncertain about the energy of a particle?

Last edited by Luxion; Dec 24th 2016 at 10:42 AM.
Luxion is offline   Reply With Quote
Old Sep 9th 2016, 12:26 AM   #2
Senior Member
 
Join Date: Apr 2015
Location: Somerset, England
Posts: 980
Perhaps Dan or Chip have better ideas by my guess is.

Note that the first statement refers to one expression of the UP
That of momentum and position.

The second statement refers an alternative expression that of energy and time, and is simply observing that given more than one available energy state, the time of a particle being in that state is uncertain.

More context might produce a better answer.

Last edited by studiot; Sep 9th 2016 at 01:32 AM.
studiot is offline   Reply With Quote
Old Sep 9th 2016, 02:56 AM   #3
Junior Member
 
Join Date: Aug 2016
Posts: 5
A minimum-uncertainty state is one in which σ x σ p = ℏ 2 σxσp=ℏ2, where σ x σx is the uncertainty in position and σ p σp is the uncertainty in momentum. ℏ / 2 ℏ/2 is the smallest possible value for the product of uncertainties in position and momentum by the Heisenberg uncertainty principle. I don't know if every minimum-uncertainty state is a gaussian, but it is certainly true that gaussians are minimum-uncertainty states.
free mobile games, free ringtones download

Last edited by NicoleJS; Dec 24th 2016 at 10:48 AM.
NicoleJS is offline   Reply With Quote
Old Sep 10th 2016, 01:06 AM   #4
Junior Member
 
Join Date: Aug 2016
Posts: 5
The minimum uncertainty refers to the product: σxσp=ℏ/2, as stated above by Lucas SV. There is no uncertainty in energy in a stationary state, as the energy is known exactly.

Tags: ringtones free download, nhạc chuông

Last edited by adamjohnson; Sep 12th 2016 at 02:57 AM.
adamjohnson is offline   Reply With Quote
Reply

  Physics Help Forum > College/University Physics Help > Quantum Physics

Tags
principle, uncertainty, understanding



Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
The Meaning of the Uncertainty Principle studiot Quantum Physics 28 Sep 2nd 2016 03:15 PM
Question About Heisenberg Uncertainty Principle omegaz Quantum Physics 1 Apr 25th 2013 06:05 AM
Photons and the uncertainty principle YellowPeril Special and General Relativity 2 Sep 16th 2009 03:29 PM
Uncertainty principle asi123 Quantum Physics 6 May 23rd 2009 03:04 PM


Facebook Twitter Google+ RSS Feed