Effektiva lösningsmetoder för Schrödingerekvationen : En jämförelse

• Main Author: Christoffer, Zakrisson
• Format: Others
• Language: Swedish
• Published: Uppsala universitet, Tillämpad beräkningsvetenskap 2013
• Subjects: Finita differenser; SBP-SAT; Schrödingerekvationen; Leap-Frog; Crank-Nicholson; Runge-Kutta; Computer and Information Sciences; Data- och informationsvetenskap; Computational Mathematics; Beräkningsmatematik
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-208878

In this paper the rate of convergence, speed of execution and symplectic properties of the time-integrators Leap-Frog (LF2), fourth order Runge-Kutta(RK4) and Crank-Nicholson (CN2) have been studied. This was done by solving the one-dimensional model for a particle in a box (Dirichlet-conditions). The results show that RK4 is the fastest in achieving higher tolerances, while CN2 is the fastest in achieving lower tolerances. Fourth order corrections of LF (LF4)and CN (CN4) were also studied, though these showed no improvements overLF2 and CN2. All methods were shown to exhibit symplectic behavior.