Direct Fisher Inference of the Quartic Oscillator’s Eigenvalues
It is well known that a suggestive connection links Schrödinger’s equation (SE) and the information-opti- mizing principle based on Fisher’s information measure (FIM). It has been shown that this entails the exis-tence of a Legendre transform structure underlying the SE. Such a structure leads to a...
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| Autores principales: | , , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2011
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/119318 |
| Aporte de: |
| Sumario: | It is well known that a suggestive connection links Schrödinger’s equation (SE) and the information-opti- mizing principle based on Fisher’s information measure (FIM). It has been shown that this entails the exis-tence of a Legendre transform structure underlying the SE. Such a structure leads to a first order partial dif-ferential equation (PDE) for the SE’s eigenvalues from which a complete solution for them can be obtained. We test this theory with regards to anharmonic oscillators (AHO). AHO pose a long-standing problem and received intense attention motivated by problems in quantum field theory and molecular physics. By appeal to the Cramer Rao bound we are able to Fisher-infer the energy eigenvalues without explicitly solving Schrödinger’s equation. Remarkably enough, and in contrast with standard variational approaches, our pre-sent procedure does not involve free fitting parameters. |
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