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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2402.06847 |
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| _version_ | 1866914673956225024 |
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| author | Nölle, Christoph |
| author_facet | Nölle, Christoph |
| contents | The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed representation of quantum mechanics as a residual theory on top of classical Hamiltonian mechanics transforms a semi-classical wave function into a slowly-fluctuating, spatially confined residual wave function. This representation is therefore well-suited for the numerical solution of semi-classical quantum problems. In this note I outline the formulation of the theory and demonstrate its applicability to a set of semi-classical scenarios, including a discussion of limitations. I work out the connection to established numerical approaches, such as the Gaussian beam approximation and the Gaussian wave packet transform by Russo and Smereka. A prototypical implementation of the method has been published as open-source software. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06847 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semi-classical Schrödinger numerics in the residual representation Nölle, Christoph Quantum Physics Computational Physics The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed representation of quantum mechanics as a residual theory on top of classical Hamiltonian mechanics transforms a semi-classical wave function into a slowly-fluctuating, spatially confined residual wave function. This representation is therefore well-suited for the numerical solution of semi-classical quantum problems. In this note I outline the formulation of the theory and demonstrate its applicability to a set of semi-classical scenarios, including a discussion of limitations. I work out the connection to established numerical approaches, such as the Gaussian beam approximation and the Gaussian wave packet transform by Russo and Smereka. A prototypical implementation of the method has been published as open-source software. |
| title | Semi-classical Schrödinger numerics in the residual representation |
| topic | Quantum Physics Computational Physics |
| url | https://arxiv.org/abs/2402.06847 |