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Direct Fisher Inference of the Quartic Oscillator’s Eigenvalues

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DOI: 10.4236/jmp.2011.211171    3,939 Downloads   6,811 Views   Citations


It is well known that a suggestive connection links Schrödinger’s equation (SE) and the information-optimizing principle based on Fisher’s information measure (FIM). It has been shown that this entails the existence of a Legendre transform structure underlying the SE. Such a structure leads to a first order partial differential 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 present procedure does not involve free fitting parameters.

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The authors declare no conflicts of interest.

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S. Flego, A. Plastino and A. Plastino, "Direct Fisher Inference of the Quartic Oscillator’s Eigenvalues," Journal of Modern Physics, Vol. 2 No. 11, 2011, pp. 1390-1396. doi: 10.4236/jmp.2011.211171.


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