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
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Lecture XVII

2. Hydrogen Atom
PHY123
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3. Concepts Electron distributions Quantum numbers, quantum state
Zeeman effect
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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
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5. Hydrogen atom Energy levels in H
n- principle quantum number – determines the energy level
What about electron distribution in atom?
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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
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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-state is possible
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Lecture XVII

8. Electron quantum state
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 z
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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
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10. Electron quantum statez
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
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11. Ground state wave function
n=1l=0ml=0y100 spin 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:
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12. Probability to find e at r
dV=4pr2dr
dP=|y|2dV= |y|24pr2dr=Prdr
Most probable radius – where Pr has maximum
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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
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14. Probability to find e at r for n=2
Most probable radius – where Pr has global maximum
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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
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Lecture XVII