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Implement a tunnneling test case, for instance in 1D with opportunities to test against some analytical case

Expand the testcases, currently testing is very minimal. Maybe use Googletest instead of Boost test.

It is possible to use a std::array or plain C array in order to save the wave-function
in each timestep. Decide on which one to use! Maybe even look in Boost if there's something
suitable to find.

At first after beginning with the 2D SSE implement the corresponding datastructures!

Implement a 2D serial worker function which uses the 2D data structures implemented
in #5

Use the current Harmonic Oscillator testcases and produce some visible results.

Orbital 3-1-1 is not consistent with representation in the literature

Orbital 4-0-0 leads to an output of 0 It works correctly

Implementation of the driven harmonic oscillator as a non automatic analyitcal test of the time dependent schrödinger equation.

Implement a shift function so that Array2D is reshuffled in a way so that the (kx,ky)=(0,0) is in the center of the grid in order to simplify the thought process to design the time evolution operators

Add the finite as well as the infinite potential well to the analytical qsystems module and maybe even to the automated unit tests. This would be an excellent way to verify the solver-correctness in a nice automated way if changes occured.

It is required to calculate a 2D integral using the trapezoidal rule.
Thus in the math namespace a corresponding function is requried

During runtime, in order to determine the energy levels, an algorithm which is able to detect peaks
is required.

Implementation of the Hydrogen Atoms time evolution in 3D

The code should be well documented so that users are able to create simulations and implement new systems using the current solvers

Problem:

• if more than 5k time-increments are calculated, then during the saving step of the correlation function fails
• Also the saving or generating the spectrum fails

Reproduced on hypnos with 24Gb of memory. Therefore, out of memory is not the problem.

After a fourier transformation has been performed on the testfunction,
one will have to apply the phase operator to it which is
exp(i (p_x^2 + p_y^2)/2M dt/2) in the frequency domain. The question
is now how to calculate the grid-spacing dpx and dpy.
From the 1D analogy: dpi = 2pi/(N_idx_i).
The question is then how does FFTW allign the results after the transformation.

2D Time evolution is currently not working properly.

The hand written MPI communication is because most of the communication interface will
be obsolete since ACCFFT will be used in later iterations.