Quiz #2. October 9
Name Topics: addition of the angular momentum states Clebsch-Gordon coefficients and 3-j symbols graphical representation matrix elements of irreducible tensor operators commutators
1. Consider a 3d state. Construct the state of the tot
Symmetries & Conservation Laws Orbital angular momentum & spin Quantum mechanics of angular momentum
Chapter 1, pages 1-10 of the Lectures on Atomic Physics 1Chapter 6, pages 207-223 of QM by Jasprit Singh 207Atomic many-body theor
Lecture #4 Hydrogen-like atom Special hydrogenic systems
How does one solve the Shrdinger equation? (Time independent potential)
$ % & # '
/ ' 0" #
Spherically symmetric potential
3 # z r
' 5 #
Postulates of quantum mechanics Uncertainty relations Hydrogen-like atoms Addition of angular momenta Dipole transitions
What does a physical theory involves?
How are the problems solved?
Postulates of quantum mechanics
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Second quantization Normal order and expectation values Wicks theorem Wick
Chapters 3 and 4, pages 95-99 Lectures on Atomic Physics 95Chapter 11, pages 241-246, Atomic many-body theory 241manyI. Lindgren and J. Morrison
October 9 October 16
Lectures #10 and #11
Identical particles Bosons and fermions Slater determinants Evaluation of one and two-particle matrix elements twoHelium atom: Applications of perturbation theory and Variational method
Chapter 10, pages 469-477,
Self-consistent fields Self-
October 31 November 4,6
Hartree-Fock equations: He-like systems HartreeHeHartree-Fock equations: closed-shell systems Hartreeclosed-
Chapter 3, pages 61-77, Lectures on Atomic Physics 61-
Quiz #3. November 11
Topics: second quantization expectation values Wicks theorem Coulomb matrix elements HF equations
1. Apply Wicks theorem to write the operator product ak al ai a j as a sum of normal-ordered terms.
Calculate the exp
Total: 80 points Need: 50/80 points. The remaining points (over 50) will be counted as bonus points. Problems which may require longer time are marked with *.
1. Examine the following list of the nlj designations, where n is the pri
Quiz #1. September 9
Name Topics: fundamentals of quantum mechanics, hydrogenic systems, angular momentum and addition of angular momenta, LS and jj coupling, and dipole transitions. 1. List one effect which is not explained by classical physics. 2. List
1. Derive the formula (to first order) for an energy shift of the ground state of hydrogen due to
gravitational interaction between proton and electron. Determine the value of the relative shift (calculate the ratio of the resultin
Addition of the angular momentum states Clebsch-Gordon coefficients & 3j symbols Irreducible tensor operators Wigner-Eckart theorem Graphical representation 6j symbols
Chapter 1, pages 11-20, 95-98 of the Lectures on Atomic Physics