Mesoscopic devices, such as nano-wires, are of interest for the next step in creating spintronic devices. With the ability to manipulate electrons and their spin, spintronic devices may be realised. To that end the different effects found in low-dimensional devices must be studied and understood. In this thesis  the influence that lateral spin-orbit coupling (LSOC) has on a nanowire, with asymmetrical confinement potential, is studied. The nanowire is studied through a numerical approach, using the Hartree-Fock method with Dirac interactions to solve the eigenvalue problem of an idealised infinite nanowire. The nanowire has a split-gate that generates the electrostatic asymmetrical confinement potential. It is found that the lateral spin-orbit coupling has little to no effect without any longitudinal effects in the wire, such as source-drain bias. The electrons will spontaneously create spin-rows in the device due to spin polarization. The spin polarization is triggered by using LSOC, numerical noise or from a weak magnetic field. / Mesoskopiska anordningar, som nano-trådar, tros vara ett viktigt steg för att skapa spinnelektronik. För att kunna skapa spinnelektronik behövs kunskap om hur elektroner kan manipuleras. Generellt måste därför existerande fenomen i nanoelektronik studeras. I denna avhandling studeras hur ''lateral spin-orbit koppling'' (LSOC) influerar en nanotråd som har en asymmetrisk potentialbarriär. Hartree-Fock metoden, med Dirac potential för elektron-elektron interaktioner, användes för att beräkna energinivåerna för en idealisk, oändligt lång nanotråd. Nanotråden har en split-gate som alstrar den elektrostatiska, asymmetriska potentialbarriären. "Lateral spin-orbit koppling" visar sig ha minimal effekt då longitudinella effekter, exempelvis spänning, saknas. Elektronerna placerar sig spontant i spinn-rader i tråden vid spontan spinn polarisation. Spinn polarisationen sätts igång av LSOC, numeriska störningar eller från svagt pålagt magnetfält.

Understanding the complexities of the interior of planets and stars requires the help of analyzing the effects of high pressures on certain elements believed to be found within. The Hartree-Fock method uses the Schr¨odinger equation, Kummer’s differential equations and a confinement potential to simulate an atom being squeezed to high pressures. The Hartree-Fock method was used to calculate the total energies of atoms. After being compared to Gaussian03 and VASP, the results were deemed accurate. It was also observed that the pressure versus density data closely approximated those pairs found in outer space in the interiors of, for example, Jupiter.