Download Course Syllabus and Assignment 1

Physics 601, Advanced Atomic Physics, Spring 2008
Instructor: Joseph Macek
Time: M–W–F: 9:05-9:55
Place: Phy 512
Text: Theoretical Atomic Physics, by Harald Friedrich, Springer publishing co. 1991,1998,
2002.
Jan 9, 2008.
I.
REVIEW OF NON-RELATIVISTIC QUANTUM MECHANICS
A.
Review of the harmonic oscillator
B.
The square well in three dimensions
1.
Bound states
2.
Continuum states
3.
Resonances
C.
Coulomb potential
D.
Quantum theory of angular momentum (?)
E.
Approximation methods (?)
1.
Time-independent perturbation theory
2.
Variational methods
3.
WKB and semiclassical methods
II.
ATOMS AND IONS
A.
One-electron species
B.
Dirac’s equation
1.
Solutions for a radial potential
2.
Solutions for the hydrogen atom
C.
Non-relativistic approximation
1.
One-electon species
2.
Many-electron species
D.
Many-electron systems
1.
Pauli principle and Slater determinants
2.
Matrix elements with Slater determinants
E.
Atomic shell structure and independent particle models
1.
Classification of atomic levels
2.
Hund’s rules
3.
Hartree-Fock theory
4.
Thomas-Fermi Model and Density Functional Theory
III.
A.
ELECTROMAGNETIC TRANSITIONS AND PHOTONS
Photons
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B.
Emission and absorption of photons
B. Emission and absorption of photons
IV. ATOMIC SPECTRA
IV. ATOMIC SPECTRA
A. The quantum defect
A. The quantum defect
B. Coupled channels and resonances
B. Coupled channels and resonances
V. ATOMIC SCATTERING
V. ATOMIC SCATTERING
VI. TIME-DEPENDENT PROCESSES
VI. TIME-DEPENDENT PROCESSES
A. Electromagnetic fields
A. Electromagnetic fields
B. Ion-atom collisions
B. Ion-atom collisions
HaraldFriedrich
THEORETICAL
ThirdEdition
Note on text: There may be used versions of editions 1 and 2 available. These are also
Notes on text: There may be used versions of editions 1 and 2 available. These are
acceptable, however the first edition lacks answers to the problems.
acceptable, however, the first edition lacks answers to the problems.
Course organization:
Course organization:
There will be a weekly homework assignment, with homework collected on Monday of
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There will be a weekly homework assignment, with homework collected on Monday of
each week. The homework will be graded and returned the same week. Homework counts
30% towards the final grade. A midterm exam at a date suitable for the class will be given.
It will also count 30% towards the final grade. A final exam will count 40% towards the
course grade.
First assignment: Read the following sections from chapter I.
1.1, 1.2.1, 1.2.3, 1.3.1,1.3.2, 1.3.3, 1.3.4, 1.5.3, 1.6.1, 1.6.2, 1.6.3, 1.7, 1.7.1, 1.7.2, 1.7.3.
First problem assingment:
Atomic units with ~ = me = e = 1 are used in this course. In these units the unit of
energy is 27.21 eV. In the problems below take the reduced mass µ = 1 a. u.
1. For a 1-dimensional harmonic oscillator with ω = 1/2 a. u. and state vectors |ψn >
compute the matrix element < ψn0 |x|ψn > for all n and n0 .
2. For the 1-dimensional harmonic oscillator ω = 1/2 a. u. and state vectors |ψn >
compute the matrix element < ψn0 |px |ψn > for all n and n0 . In coordinate space
px = −i~
∂
∂x
.
3. Compute the value of the energy eigenvalues of the ` = 0 bound states of a spherical
potential
V (r) = −V0 ,
V (r) = 0,
r ≤ r0
r > r0
(1)
for mass µ = 1 a. u., V0 = 4 a. u. and r0 = 3 a. u. How many bound states does this
potential have?
4. For the square well in the previous problem, compute the value of the phase shift δ(E)
at E = 0. Plot the radial function φ(r) vs r for 0 < r < 6 a. u.
5. Write down an expression for the normaiized ground state wave function φ(r) of a
hydrogenic ion with nuclear charge Z. Verify by direct substitution in the Schrödinger
equation that this function is an energy eigenfunction and extract the energy eigenvalue.
Compute the expectation value of r2 and deduce the mean value of r2 for the ground state.
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