Effektiva lösningsmetoder för Schrödingerekvationen: En jämförelse
Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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.
Place, publisher, year, edition, pages
2013. , 14 p.
TVE, TVE 13010 maj
Finita differenser, SBP-SAT, Schrödingerekvationen, Leap-Frog, Crank-Nicholson, Runge-Kutta
Computer and Information Science Computational Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-208878OAI: oai:DiVA.org:uu-208878DiVA: diva2:655075
Master Programme in Engineering Physics
Mattsson, Ken, Ph.D.