Phys621: (Fall 2006)
Quantum Mechanics

Course calendar:

There is a brief description of the content for each lecture, together with links to handouts (HW, etc). The references (in red) point to parts in the text and reference books that may be helpful in complementing your lecture notes.
Th 8/31
  • General information.

  • Why Quantum Mechanics? 
    

  •  Historical foundations

        -  Lecture notes  
    
  
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  Tu
  9/5
  

No class this week  --- I am at a
workshop: 

International Workshop:
Density functional theory
meets strong correlation 

  

    

    
  Th
  9/7
  
  

    

    
    
     
    
    

    
  Tu
  9/12
  

  •  SG experiment

        -  Sakurai 1.1  
    

        -  An easy-reading on-line intro on the SG.
     
  
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  Th
  9/14
  

  •  Schrodinger Equation and wave functions

        -  Lecture notes; Sakurai 1.3  
    

  •  Introduction to Dirac notation

        -  Sakurai 1.2  
    

 
Homework Assignment 1 
out.
  
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  Tu
  9/19
  

  •  Dirac notation

        -  Sakurai 1.2  
    
  
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  Th
  9/21
  

  •  Base kets and matrix representation

        -  Sakurai 1.3  
    

  •  Measurements and observables

        -  Sakurai 1.4  
    
  
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  Tu
  9/26
  

  •  Spin 1/2 systems -- formal development.

        -  Sakurai 1.3, 1.4  
    

  •  Compatible and incompatible observables.

        -  Sakurai 1.4  
    

-- Homework Assignment 2 out.
  
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  Th
  9/28
  

  •  Compatible and incompatible observables, cont'd

        -  Sakurai 1.4  
    

  •  The uncertainty relation

        -  Sakurai 1.4  
    

  •  Change of basis

        -  Sakurai 1.5  
    

  •  Additional Reading: Diagonalization and Unitary equivalent operators
        -  Sakurai 1.5  
    
  
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  Tu
  10/3
  

  •  Change of basis, cont'd

        -  Sakurai 1.5  
    

  •  Position basis and wave function, revisited

        -  Sakurai 1.6, 1.7  
    

  •  Translation and momentum.

        -  lecture notes; Sakurai 1.6 
    
  
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  Th
  10/5
  

  •  Translation and momentum, cont'd

        -  lecture notes; Sakurai 1.6 
    

-- Homework Assignment 3 out.
  
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  Tu
  10/10
  

  •  Wave function and the Schrodinger Eq.

        -  Sakurai 1.7, including Gaussian wave packets 
    

  •  Time evolution operator.

        -  Sakurai 2.1 
    
  
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  Th
  10/12
  

  •  Quantum dynamics.

        -  Sakurai 2.1; ; lecture notes 
    

  •  Time-dependent Schrodinger equation

        -  Sakurai 2.4 
    

  
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  Tu
  10/17
  
Fall break
  

    

    
  Th
  10/19
 

  •  Axioms of quantum theory

        -  Lecture notes 
    

  •  Heisenberg picture, Ehrenfest's theorem

        -  Sakurai 2.2 
    

-- midterm out; due on Th 10/26 out.
  
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  Tu
  10/24
  

  •  Propagators and path integrals.

        -  Sakurai 2.5; lecture notes 
    
  
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  Th
  10/26
  

  •  Propagators and path integrals.

        -  Sakurai 2.5; lecture notes 
    

-- Homework Assignment 4 out.
  
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  Tu
  10/31
  

  •  Path integrals.

        -  Sakurai 2.5; lecture notes 
    

  •  Intro to Simple Harmonic oscillator

        -  lecture notes; Sakurai 2.3 
    
  
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  Th
  11/2
  

  •  Simple Harmonic oscillator

        -  lecture notes; Sakurai 2.3 
    

  •  Algebraic method (SHO)

        -  Sakurai 2.3; lecture notes 
    
  
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  Tu
  11/7
  

  •  Coherent states

        -  Sakurai 2.3 
    

  •  Time evolution of coherent states

        -  Sakurai 2.3; lecture notes 
    

  •  SHO in 2-D

    

-- Homework Assignment 5 out.
  
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  Th
  11/9
  

  •  Electron in a magnetic field

        -  Sakurai 2.6; lecture notes 
    
  
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  Tu
  11/14
  

  •  Flux quantization.

        -  lecture notes; Prob 2.25 
    

  •  The Aharonov-Bohm effect

        -  Sakurai 2.6 
    
  
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  Th
  11/16
  

  •  Rotations (regular).

        -  Sakurai 3.1; lecture notes 
    

  •  Intro. to QM Angular Momentum.

        -  Sakurai 3.1; lecture notes 
    
  
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    Fr
  11/17
  

  •  Make-up class -- problem session

-- in Jones Hall Room 307

    

-- Homework Assignment 6 out.
  
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  Tu
  11/21
  

  •  QM Angular Momentum.

        -  Sakurai 3.1; lecture notes 
    

  •  First example -- spin-1/2 systems.
  
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  Th
  11/23
  
Thanksgiving
  

    

    
    
     
    
    

    
  Tu
  11/28
  

  •  Second example -- orbital angular momentum.

        -  Sakurai 3.6; lecture notes 
    
 
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  Th
  11/30
  

  •  Eigenvalues and eigenstates of angular momentum.

        -  Sakurai 3.5  
    

  •  Additional Reading: SO(3), SU(2), and Euler rotations.

        -  Sakurai 3.3  
    

-- Homework Assignment 7 out. 
  
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  Tu
  12/5
  

  •  Spherical harmonics.

        -  Sakurai 3.6 
    

  •  Central potentials; Hydrogen atom

        -  lecture notes. 
    
 
  •  Introduction to the addition of Angular momenta.

        -  Sakurai 3.7; lecture notes 
    
  
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  Th
  12/7
  

  •  Addition of Angular momenta -- C-G coefficients.

        -  Sakurai 3.7 
    

  •  Reading materials: Bell's inequality
 
        -  Sakurai 3.9 
    

  •  Putting it all together

        -  lecture notes 
    
  
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