1. Quantum mechanics I Fall 2012
Physics 451
Quantum mechanics I
Fall 2012
Nov 26, 2012
Karine Chesnel

2. Test 3: Tuesday Nov 27 – Fri Nov 30 Homework HW 22 Thursday Nov 29
Quantum mechanics
Test 3:
Tuesday Nov 27 – Fri Nov 30
Homework
HW 22 Thursday Nov 29
HW 23 Monday Dec 3
HW 24 Wednesday Dec 5

3. Two-particles systems
Quantum mechanics
Two-particles systems
Pb 5.1, 5.2
Time-independent potential

4. Two-particles systems
Quantum mechanics
Two-particles systems
If we could distinguish two identical particles a a b b

5. Two-particles systems
Quantum mechanics
Two-particles systems
In QM: we can not distinguish two identical particles a b
Normalization Pb 5.4

6. Pauli exclusion principle:
Quantum mechanics
Bosons and fermions
S = integer
Bosons:
Fermions:
S = half-integer
Pauli exclusion principle:
Two identical fermions can not occupy the same state

7. Two-particles system Symmetrization requirement: Symmetric:
Quantum mechanics
Two-particles system
Symmetrization requirement:
Symmetric:
Antisymmetric:

8. Two particles system For distinguishable particles
Quantum mechanics
Two particles system
For distinguishable particles
For indistinguishable (identical) particles
symmetrical
antisymmetrical
Example: 2 particles in infinite square well 11

9. Separation distance For distinguishable particles
Quantum mechanics
Separation distance
For distinguishable particles
For indistinguishable particles

10. Exchange forces Bosons are closer than if they were distinguishable
Quantum mechanics
Exchange forces
Bosons are closer than if they were distinguishable
Fermions are farther apart than if they were distinguishable

11. Exchange forces Attraction force Symmetrical state: Covalent bound
Quantum mechanics
Exchange forces
Attraction force
Symmetrical state:
Covalent bound
Repulsion force
Antisymmetrical state

12. Two electrons Total state antisymmetrical Spin state: singulet
Quantum mechanics
Two electrons
Total state antisymmetrical
Spatial state symmetrical
Spin state: singulet
antisymmetrical
Attraction force
Covalent bound
Pb 5.6

13. Quiz 29 If two electrons would occupy a triplet state (S=1)
Quantum mechanics
Quiz 29
If two electrons would occupy a triplet state (S=1)
what can we say about their spatial wave function?
It is antisymmetric (antibounding)
It is symmetric (bounding)
It could be both

14. Homework Pb 5.1: Pb 5.2: Pb 5.6: Quantum mechanics Reduced coordinates