Solving simple quantum systems using bootstrapping

Date

2024-8-22

Author

Nohutçu, Ali Ulvi

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In this thesis, we investigate the application of the bootstrap method, which is a numerical approach for identifying energy eigenstates in quantum systems developed in a series of recent articles in the literature, to solve several quantum mechanical systems. First, we establish the theoretical background of the bootstrap method, focusing on the Hamburger moment problem and how it can be related to quantum mechanical systems. We obtain the generalized moment recursion relation and discuss the parameters needed to initialize it. We discuss possible problems with the algorithm and offer optimizations that use the bootstrapping method combined with numerical methods. As examples, we apply the method to the Simple Harmonic Oscillator, the Anharmonic Oscillator, and the Hydrogen atom, then compare the results to theoretical values and evaluate the effectiveness of the method.

Subject Keywords

Bootstrap method, Moment problems, Simple harmonic oscillator, Anharmonic oscillator, Hydrogen atom

URI

https://hdl.handle.net/11511/111038

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Graduate School of Natural and Applied Sciences, Thesis