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

2hpx x

Heisenberg's Uncertainty Principle - applies to all “conjugate variables”

___________________________________

Position & momentum

Energy & time

2hpx x

2htE

Uncertainty Principle and the Wave Packet___________________________________

ph

2hpx x

If is large, is small

pp

x

x

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 34h2hpx 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

ph

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 vcv 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

2hpx x

2htE

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