1. Welcome back from fall break Comments on mid-term exam
PHY 741 Quantum Mechanics
12-12:50 PM MWF Olin 103
Plan for Lecture 19:
Welcome back from fall break
Comments on mid-term exam
Comments on “computational projects”
Quantum mechanics of atoms (Chapter 13)
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PHY 741 Fall Lecture 19

2. Three events this week --
+ pizza
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PHY 741 Fall Lecture 19

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5. Example: Particle of mass m confined within an finite square well:
V(x) V0 V0 x a
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PHY 741 Fall Lecture 19

6. After some algebra, we found that the energy eigenvalues E were solutions of transcendental equations:
For even parity
For odd
parity
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PHY 741 Fall Lecture 19

7. x/a
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8. x/a
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17. Picking topic for “project”
Prepare ~ 10 minute presentation to teach us (and yourself) something related to quantum mechanics
Similar effort to take-home exam
Can combine with classical mechanics project
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PHY 741 Fall Lecture 19

18. Back to the quantum mechanics of atoms
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PHY 741 Fall Lecture 19

19. Shell structure of atoms based on Hartree and Hartree-Fock treatments
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PHY 741 Fall Lecture 19

20. Shell structure of atoms Principal Quantum Angular momentum Number of
Number Quantum Number States
n= l=0 (s)
n= l=0 (s)
l=1 (p)
n= l=0 (s)
l=2 (d)
n= l=0 (s)
l=3 (f)
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PHY 741 Fall Lecture 19

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22. Self-consistent treatment of the Veff(r)
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23. Example for carbon
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PHY 741 Fall Lecture 19

24. Results for carbon 1s 2p Pnl(r) 2s E1s=-19.9 Ry E2s=-1.0 Ry
E2p=-0.4 Ry
r (Bohr)
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PHY 741 Fall Lecture 19