In quantum mechanics it is not uncommon to find analytically solved problems involvinga degree of math too advanced for most. It is often helpful to use a numerical approachto test solutions and deepen the understanding of such problems. In order to determine the validity of this approach, it is important to examine its accuracy. An exampleof this is the Landau-Zener problem, which is the topic of this thesis. It describes atwo-state quantum mechanical system that is applicable to many real world situations.The numerical method used involves propagating the wave function by calculating thetime evolution operator for numerous time steps. The accuracy using this method wasanalysed by comparing the results with the exact solution with varying parameters. Theconclusion is that the numerical solution does converge toward the known analytical solution. However, it does this with different accuracy, depending on the system parameters.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kth-349367 |
| Date | January 2024 |
| Creators | Käll, Niklas, Ulander, Emil |
| Publisher | KTH, Skolan för teknikvetenskap (SCI) |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | TRITA-SCI-GRU ; 2024:177 |
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