Vliet, Ilse van (2023) Exact solutions to the time-dependent harmonic oscillator using Hermite polynomials. Bachelor's Thesis, Applied Mathematics.
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Abstract
In this paper, we consider time-dependent harmonic oscillators and construct a solution using Hermite polynomials. In this process, we use Gaussian wave packets. Using these solutions we can find observability constants for examples on L^2(R^2). In the first part, we will go over several topics needed for the final result. This includes the Fourier transform, the Schrödinger equation, Hermite polynomials and wave packets. In the second part, we introduce a lemma about the Fourier integral operator that helps us solve differential equations with time-dependent operators with a quadratic potential and we find the observability constant for certain initial data.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Waters, A.M.S. and Koellermeier, J. |
| Degree programme: | Applied Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 26 Jan 2023 09:40 |
| Last Modified: | 26 Jan 2023 09:40 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/29164 |
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