Galilean relativity and wave-particle duality imply the Schrödinger equation
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914789698043904 |
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| author | Rigolin, Gustavo |
| author_facet | Rigolin, Gustavo |
| contents | We show that the Schrödinger equation can be derived assuming the Galilean covariance of a generic wave equation and the validity of the de Broglie's wave-particle duality hypothesis. We also obtain from this set of assumptions the transformation law for the wave function under a Galilean boost and prove that complex wave functions are unavoidable for a consistent description of a physical system. The extension to the relativistic domain of the above analysis is also provided. We show that Lorentz covariance and wave-particle duality are consistent with two different transformation laws for the wave function under a Lorentz boost. This leads to two different wave equations, namely, the Klein-Gordon equation and the Lorentz covariant Schrödinger equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15555 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Galilean relativity and wave-particle duality imply the Schrödinger equation Rigolin, Gustavo Quantum Physics High Energy Physics - Phenomenology High Energy Physics - Theory We show that the Schrödinger equation can be derived assuming the Galilean covariance of a generic wave equation and the validity of the de Broglie's wave-particle duality hypothesis. We also obtain from this set of assumptions the transformation law for the wave function under a Galilean boost and prove that complex wave functions are unavoidable for a consistent description of a physical system. The extension to the relativistic domain of the above analysis is also provided. We show that Lorentz covariance and wave-particle duality are consistent with two different transformation laws for the wave function under a Lorentz boost. This leads to two different wave equations, namely, the Klein-Gordon equation and the Lorentz covariant Schrödinger equation. |
| title | Galilean relativity and wave-particle duality imply the Schrödinger equation |
| topic | Quantum Physics High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2403.15555 |