1. Chap. 20 in Shankar: The Dirac equation
PHY 741 Quantum Mechanics
12-12:50 AM MWF Olin 103
Plan for Lecture 32:
Chap. 20 in Shankar: The Dirac equation
Some simple concepts of special theory of relativity
Energy and momentum relationships
Dirac equation for a free particle
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PHY 741 Fall Lecture 32

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PHY 741 Fall Lecture 32

3. Notions of special relativity
The basic laws of physics are the same in all frames of reference (at rest or moving at constant velocity).
The speed of light in vacuum c is the same in all frames of reference. y’ y v x x’ y’ x’ y x
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PHY 741 Fall Lecture 32

4. Lorentz transformationsy’ y v x x’ y’ x’ y x
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PHY 741 Fall Lecture 32

5. Lorentz transformations -- continued
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PHY 741 Fall Lecture 32

6. Examples of other 4-vectors applicable to the Lorentz transformation:
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PHY 741 Fall Lecture 32

7. Lorentz transformation of the velocity
For an infinitesimal increment:
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PHY 741 Fall Lecture 32

8. Lorentz transformation of the velocity -- continued
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PHY 741 Fall Lecture 32

9. Example of velocity variation with b:
ux/c
uy/c
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PHY 741 Fall Lecture 32

10. Velocity transformations continued:
Velocity 4-vector:
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PHY 741 Fall Lecture 32

11. Some details:
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PHY 741 Fall Lecture 32

12. Significance of 4-velocity vector:
Introduce the “rest” mass m of particle characterized by velocity u:
Properties of energy-moment 4-vector:
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PHY 741 Fall Lecture 32

13. Properties of Energy-momentum 4-vector -- continued
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PHY 741 Fall Lecture 32

14. Summary of relativistic energy relationships
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PHY 741 Fall Lecture 32

15. How do these relationships effect quantum mechanics?
Focusing on treatment of Fermi particles
Non-relativistic mechanics
Relativistic mechanics
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PHY 741 Fall Lecture 32

16. Relativistic relationships – continued
Ref: J. J. Sakurai, Advanced Quantum Mechanics
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PHY 741 Fall Lecture 32

17. Relativistic relationships – continued
Ref: J. J. Sakurai, Advanced Quantum Mechanics
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PHY 741 Fall Lecture 32

18. Relativistic relationships – continued
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PHY 741 Fall Lecture 32

19. Four component wavefunction of free Fermi particle
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PHY 741 Fall Lecture 32

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22. What does this all mean?
11/17/2017
PHY 741 Fall Lecture 32