1 / 10

Physics 3313 - Lecture 13

Physics 3313 - Lecture 13. Monday March 23, 2009 Dr. Andrew Brandt. Loose ends from Ch. 4 Nuclear Motion+Lasers QM Particle in a box Finite Potential Well. Nuclear Motion. In Bohr atom, we have implicitly assumed nucleus is fixed, since we only considered electron KE.

ramiro
Download Presentation

Physics 3313 - Lecture 13

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Physics 3313 - Lecture 13 Monday March 23, 2009 Dr. Andrew Brandt • Loose ends from Ch. 4 Nuclear Motion+Lasers • QM Particle in a box • Finite Potential Well 3313 Andrew Brandt

  2. Nuclear Motion • In Bohr atom, we have implicitly assumed nucleus is fixed, since we only considered electron KE. • Since nucleus does not (quite) have infinite mass, it will have motion if the total momentum of the atom is zero • pe+pN=0 so pe=-pN with KEN= p2/2M • where the reduced mass is defined as • For M=m get but in the case of Hydrogen so • What about heavier atom? 3313 Andrew Brandt

  3. Electron Transition Example • An electron makes a transition from n=2 state to n=1, find ,  of emitted photon 3313 Andrew Brandt

  4. Laser • Light Amplification by Stimulated Emission of Radiation • laser light is monochromatic (one color), coherent (all in phase), can be very intense, small divergence (shine laser on mirror left on moon) [I knew I forgot something] 3313 Andrew Brandt

  5. Three Level Laser 3313 Andrew Brandt

  6. Particle in a Box Again • http://user.mc.net/~buckeroo/PODB.html • Solutions: • Would have cos also, but boundary condition at x=0 implies coefficient =0 • Use boundary condition at x=L gives • which is equivalent to classical expression • Final wave function 3313 Andrew Brandt

  7. Particle in a Box Example • What is the probability that a particle in a box is between 0.45L and 0.55L for n=1? n=2? • What is the classical answer? • 10% since this is 1/10 of the length of the box • with • Integrating gives • for n=1 P=0.198 (about twice expectation), while for n=2 P=0.0065 • Does this make sense? Wave Function Probability 3313 Andrew Brandt

  8. Particle in a 3-D Box • Need 3-D Schrodinger Equation: • Factorizes into product of 3 1-D equations so • Note 3-fold degeneracy for one dimension in n=2 state • For rectangular box 3313 Andrew Brandt

  9. Finite Potential Well • Classically if E<U than particle bounces off sides, but quantum mechanically, particle can penetrate into regions I and III • For I rewrite as • With • Solutions are and • What about in the box? Since U=0 with (this is similar to infinite potential well, aka particle in box) 3313 Andrew Brandt

  10. Finite Well BC • At x=- =0 so for D must be 0 ,so • Similarly at x=+ =0 so for F must be 0 and • Finally what about boundary conditions for ? Is it 0 at x=0? • Nope at x=0 • And at x=L • But so too many unknowns! Should we quit? • Need other constraints. Derivatives must also be continuous (match slopes) • After some math again get specific energy levels, but wavelengths a little longer than infinite well and from De Broglie, this means momentum and thus energy is smaller 3313 Andrew Brandt

More Related