Today

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