lecture6

lecture6 - 5.61 Fall 2007 Lecture #6 page 1 WAVE-PARTICLE...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
5.61 Fall 2007 Lecture #6 page 1 WAVE-PARTICLE DUALITY of MATTER Consequences (II) ! Heisenberg Uncertainty Principle Δ x Δ p x 2 Consider diffraction through a single slit D M λ = s M D = s light, s l peak-null D distance x Coming out of the slit, the electrons spread out to form a diffraction pattern with width . v ! v ! x v Δ This means the electrons must go through the slit with some range of velocity components v x Now consider a beam of electrons with de Broglie wavelength . The slit restricts the possible positions of the electrons in the x direction: at the slit, the uncertainty in the electron x-position is xs Δ =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
! 5.61 Fall 2007 Lecture #6 page 2 Δ v D λ x = = v ! s Δ x Δ x Δ v x = v or Δ x Δ p x = p h But from deBroglie = p Δ x Δ p x = h So the position and momentum of a particle cannot both be determined with arbitrary position! Knowing one quantity with high precision means that the other must necessarily be imprecise! The conventional statement of the Heisenberg Uncertainty Principle is Δ x Δ p x 2 (depends on how “uncertainty” is defined: 1/e half-width, FWHM, etc.) Uncertainty can always be larger than ! 2 , but not smaller.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/01/2011 for the course MATH 1090 taught by Professor Greenwood during the Fall '08 term at MIT.

Page1 / 5

lecture6 - 5.61 Fall 2007 Lecture #6 page 1 WAVE-PARTICLE...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online