README.md

computationalphysics2021

Repository for the course Computational Physics help by Prof. Pederiva at unitn.

Exercise 1: Scattering of H atoms an Kr atoms

1. 1D harmonic oscillator solution with Numerov method
2. 3D harmonic oscillator with the same method
3. Implementation of the recursive formulas for the Bessel functions
4. Rescaling of the problem units
5. A mathematical proof
6. Modification of Numerov code for interatomic potential and calculation of the phase shift
7. Calculation of the cross section

Exercise 2: Mean Field Methods and Hartree Fock

1. Calculation of Hydrogen ground state via variational procedure
2. Graphical representation of Hydrogen WF and electronic density
3. Calculation of Helium ground state energy via Hartree-Fock method.
4. Graphical representation of Helium WF and electronic density
5. Berillium ground state without contraction
6. Graphical representation of Berillium WFs and electronic densities

Exercise 3: DFT for clusters of alkali atoms

TODO

1. Write a program to compute the densities in the uncorrelated and non-interacting electrons case
2. Self consistent procedure acconting for direct, exchange and correlation terms.
3. Polarisation calculation

Exercise 4: Variational MC for Superfluid He

3. Setup of the initial configuration of the system for the simulation.

TODO

1. Write down explicit expresison for the local kinetic energy in two different ways as shown in the lecture. (to be corrected...)
2. Work out hbar/2m when using the proper energy and length units of the problem (to be corrected...)
3. Metropolis algorithm to sample the square modulus of the WF and compute the energy. Minimise the energy. (waiting for the previous two points to compute local kinetic energy...)
4. Repeat the simulation for other 2 densities and find the minimum of the density. (Once point 4 is done, this is done as well...)