Uncertainty Principle
15
Heisenberg's Uncertainty Principle _________________________________ __ The Uncertainty Principle is an important consequence of the wave-particle duality of matter and radiation and is inherent to the quantum description of nature Simply stated, it is impossible to know both the exact position and the exact momentum of an object simultaneously
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The Uncertainty Principle is an important consequence of the wave-particle duality of matter and radiation and is inherent to the quantum description of nature
Transcript of Uncertainty Principle
Heisenberg's Uncertainty Principle___________________________________
The Uncertainty Principle is an important consequence of the wave-particle duality of matter and radiation and is inherent to the quantum description of nature
Simply stated, it is impossible to know both the exact position and the exact momentum of an object simultaneously
A fact of Nature!
Heisenberg's Uncertainty Principle__________________________________
Uncertainty in Position :
Uncertainty in Momentum:
x
xp
2
hpx x
Heisenberg's Uncertainty Principle - applies to all “conjugate variables”
___________________________________
Position & momentum
Energy & time
2
hpx x
2
htE
Uncertainty Principle and the Wave Packet___________________________________
p
h
2
hpx x
If is large, is small
p
p
x
x
x p
Some consequences of the Uncertainty Principle
___________________________________• The path of a particle (trajectory) is not well-
defined in quantum mechanics
Electrons cannot exist inside a nucleus
Atomic oscillators possess a certain amount of energy known as the zero-point energy, even at absolute zero.
Why isn’t the uncertainty principle apparent to us in our ordinary experience…?
Planck’s constant, again!! ___________________________________
Planck’s constant is so small that the uncertainties implied by the principle are also too small to be observed. They are only significant in the domain of microscopic systems
J.s10x6.6 34h2
hpx x
Summary___________________________________
Matter and radiation have a dual nature – of both wave and particle
The matter wave associated with a particle has a de Broglie wavelength given by
p
h
Summary (contd.)___________________________________
A (localized) particle can be represented by a group of waves called a wave packet
The group velocity of the wave packet is
The phase velocity of the wave packet is v
cv p
2
vvg
Summary (contd.)___________________________________
Heisenberg’s uncertainty principle is an important consequence of the wave-particle duality of matter and radiation and is inherent to the quantum description of nature
It applies to all conjugate variables and also to the notion of the wave packet
2
hpx x
2
htE
Are matter waves for real?! __________________________________
In 1927 Davisson and Germer showed that electrons can diffract – they act like waves
Big application – Electron Microscopes
Are matter waves for real?! __________________________________
Double –slit experiment with electrons (1989) (www.hqrd.hitachi.co.jp/em/doubleslit.cfm)
Are matter waves for real?! __________________________________
Today, advances in technology have led to matter wave interference experiments being demonstrated successfully not only with electrons but neutrons, atoms, and big and small molecules!
Infact, the largest molecule showing interference has almost a 100 atoms!
Are matter waves for real?! __________________________________
C60 molecules (Fullerenes or Bucky Balls) have a wave nature! (A. Zeilinger et al, Vienna, 1999)
Biomolecules have it too! Porphyrin
(2003)
Are matter waves for real?! __________________________________
What next? – Matter wave interference for a Virus?!
Matter waves are real…. _______________________________
If there is wave, there must be a wave equation………
The Schrödinger Equation
