C++ Lab Course - Seminar topics

Wave function class
A wave function is the following object
• It has up to three coordinate axes which also defines a discretization by a product basis (the
axis class will be supplied)
• It has a time
• We can form the scalar product of two wave functions.
• We can apply the overlap matrix and the inverse of the overlap matrix to the wave function.
Operator class
Operator representations on product basis sets. This is an important and large class, the task can
be split into smaller parts.
• An operator is constructed given a set of axes and a string that defines the operator. A typical
string could be the kinetic energy in 2-d polar coordinates φ, ρ in the tensor-product form
kin = ’+1/2(|)x(d|d) +1(d|d)x(|1/q^2|)’
or general potentials, e.g the harmonic oscillator:
pot = ’harmonic(kappax,kappay)’
for
pot(x, y) = κ x x 2 + κ y y 2
• An operator can be applied to a wave function, the result is a wave function.
• Operators on finite-element basis sets are stored piecewise for each product of finite elemetns.
• Tensor product operators are stored as the individual factors.
• Potentials are stored by their values on quadrature points and by the transformation matrices
from the basis set to the quadrature points (compare the discussion of DVR).
Timer routines
Functionality like in “mytimer.py”: find C++ class with this functionality or translate the python
code. We want
• Minimal timer overhead — timer operation must be fast!
• Option to switch off the timer (to reduce any possible overhead to the absolute mininum).
• Progress monitor: let the timer print a “.” or “-” if more than n seconds that have elapsed
since it was last called last time.
Time propagator class
A time-propagator takes as an argument and operator, wave function, a new time, and an accuracy
parameter. Advances the wave function from its current time to the new time by solving the TDSE
with the given operator. Controls the accuracy.
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