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Notes
The links below give pdfs to the
required reading for the course. Any changes of these notes from their form as
of January 5, 2017 will be dated.
Wave mechanics
Historical
overview (modified 1/12/2017)
Wave
mechanics (modified 1/16/2017)
Phase
velocity and group velocity (modified 1/20/2017)
Solutions
in 1-dimensional wave mechanics (modified 1/25/2017)
Spin
The
effect of measurement of a quantum system (modified 1/26/2017)
The
curious properties of spin (modified 2/2/2017)
Bell's
theorem and the EPR paradox (modified 2/5/2017)
John
S. Bell, On the Einstein Podolsky Rosen paradox
N. David Mermin,
Is the moon there when nobody looks?
Reality and the quantum theory
Dirac notation for quantum
mechanics
Quantum
states as vectors (modified 2/16/2017: Section 5
added)
Measurements,
Observables and the Uncertainty Relations
Change
of basis (modified 7 PM
2/21/2017)
Symmetries (modified 2/23/2017)
Discrete
Symmetries (modified 3/3/2017)
Quantum
Dynamics (modified 3/10/2017)
An
example in quantum dynamics: Neutrino oscillations (modified 3/10/2017)
Midterm
QMSHO (modified 3/27/2017)
Irreducible representations
of angular momentum
Angular
momentum (modified 4/9/2017)
All
Representations for Rotations (4/9/2017)
Orbital
angular momentum and the spherical harmonics (modified 4/24/2017 (finally!)
)
Addition
of angular momentum (modified 4/24/2017)
Tensor
operators and the Wigner-Eckart theorem
More
on irreducible tensor operators and a different proof of the Wigner-Eckart theorem
Hydrogen
The
radial wave function, quantization, and Laguerre
polynomials
Stationary
state perturbation theory; fine and hyperfine structure
Degenerate
stationary state perturbation theory
Problems:
Zeeman and Stark effects in hydrogen
Quantum field theory
Quantization
of the Klein-Gordon field (posted 4/21/2017. Detailed notes)
Hamiltonian
operator and states of the Klein-Gordon field (posted 4/21/2017. Detailed
notes)
The
Dirac equation (posted 4/21/2017. Detailed notes)
Permutation symmetry,
statistics, and helium
Permutation
symmetry and the spin-statistics theorem, with the example of helium
Notes from 2013
Week 1:
More than you
need to know on Vector Spaces
Week 2:
Measurements,
Observables and the Uncertainty Relations
Weeks 3, 4:
Spin States (1/22)
Change of basis (1/27)
Continuum bases (1/27)
Weeks 5, 6:
Quantum
Dynamics (2/7) update
(2/11) update (2/17)
Weeks 6, 7, 8:
Quantum simple
harmonic oscillator
(2/17)
The wave
equation (2/17)
Solutions to
the wave equation (2/24)
REVIEW FOR
MIDTERM EXAM (2/27)
Week 9:
Angular
momentum (3/18)
Orbital angular
momentum and the spherical harmonics (3/28)
Addition of
angular momentum
(4/2)
Is the moon
there when nobody looks?
(4/12)
Bell's theorem (4/10)
Neutron
Interference (4/19)
Tensor
operators and the Wigner-Eckart theorem
(4/19)
More on irreducible
tensor operators and a different proof of the Wigner-Eckart
theorem (4/19)
Symmetry
(4/23)
REVIEW TOPICS
FOR FINAL EXAM (4/25)
To be referenced later:
Notes on irreducible tensors and the Wigner-Ekhart theorem:
Notes on the splitting between the lowest even
and odd parity states of the quantum double well potential:
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