1 / 15

Today

Today. Monday, March 21, 2005 Event: The Elliott W. Montroll Lecture Speaker: Prof. David Gross, University of California, Santa Barbara Title: The future of physics (25 questions that might guide physics in the next 25 years)

Download Presentation

Today

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. Today • Monday, March 21, 2005 • Event: The Elliott W. Montroll Lecture • Speaker: Prof. David Gross, University of California, Santa Barbara • Title: The future of physics (25 questions that might guide physics in the next 25 years) • Talk:3:45 pm, Hoyt Hall Tea:3:15 pm, B&L Foyer Recipient of the 2004 Nobel Prize In Physics Lecture XVII

  2. Hydrogen Atom PHY123 Lecture XVII

  3. Concepts • Electron distributions • Quantum numbers, quantum state • Zeeman effect Lecture XVII

  4. Schrödinger equation for Hydrogen atom • Potential energy – electron is in Coulomb’s potential of the nucleus: • Spherically symmetric potential • 3-D Schrödinger's equation Lecture XVII

  5. Hydrogen atom • Energy levels in H • n- principle quantum number – determines the energy level • What about electron distribution in atom? Lecture XVII

  6. Electron distributions • Same n, different shapes. Other quantum numbers play a role • Quantum state of electron in atom is defined by a set of 4 numbers • Principle quantum number n • Orbital quantum number l • Magnetic quantum number ml (same as lz) • Spin projection ms • Wave functions depend on 3 quantum numbers Lecture XVII

  7. Electron quantum state • Principle quantum number n=1,2,3,4,… • determines energy level, higher E for higher n • Orbital quantum number l • For each n l can be 0,1,2,3, …(n-1) • l states are leveled by letters • s: l=0; p: l=1; d: l=2; f: l=3; g:l=4 • E.g. n=5, then l can be 0, 1, 2, 3, 4 • Possible l states are s,p,d,f,g • n=1, only l=0 s-stateis possible Lecture XVII

  8. Electron quantum state z • Orbital quantum number is a vector length l • Orbital angular momentum: • Its projection on z axis is Lz =mlh another q.n. – magnetic quantum number ml • ml can be only integer Lecture XVII

  9. Zeeman effect • Normally energy does not depend on ml, but under magnetic field energy levels split- fine structure • Magnetic moment (dipole) associated with orbital angular momentum • Potential energy of the magnetic dipole in magnetic field Lecture XVII

  10. Electron quantum state z • All electrons have spin=1/2 • It is a vector • Its projection on z axis is another q.n. – spin ms • ms can be only Lecture XVII

  11. Ground state wave function • n=1l=0ml=0y100spin could be up or down • No “preferred direction”  system is spherically symmetric  expect wave function to depend only on r • Not true if l≠0 • n=10 knots • Wave function • Bohr’s radius: Lecture XVII

  12. Probability to find e at r • dV=4pr2dr • dP=|y|2dV= |y|24pr2dr=Prdr • Most probable radius – where Pr has maximum Lecture XVII

  13. n=2 wave function • n=2l=0,1 • First consider y200 • Still no “preferred direction”  system is spherically symmetric  expect wave function to depend only on r • n=21 knots • Wave function Lecture XVII

  14. Probability to find e at r for n=2 • Most probable radius – where Pr has global maximum Lecture XVII

  15. n=2 wave function • n=2l=0,1 • Now consider y21m • There is a “preferred direction” – direction of vector L system is NOT spherically symmetric, but axial symmetry is there  expect wave function to depend not only on r Lecture XVII

More Related