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

Info icon This 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 λ = s λ D = s light, λ s l peak-null D distance x Coming out of the slit, the electrons D spread out to form a diffraction pattern with width D . x v ! v ! x v Δ This means the electrons must go through the slit with some range of velocity components v x x Now consider a beam of electrons with de Broglie wavelength λ . 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 =
Image of page 1

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

View Full Document Right Arrow Icon
! 5.61 Fall 2007 Lecture #6 page 2 Δ v D λ λ x = = v ! s Δ x Δ x Δ v x = λ v or Δ x Δ p x = λ p h But from deBroglie λ = 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.)
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern