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Deducing the Schrödinger equation from minimum χ2


The most unbiased probabilistic model for the possible values of a characteristic of a quantum system subject to the constraints represented by some known mean values characterizes the system in a steady-state condition. We suppose that random fluctuations alter such a steady-state condition. The probability distribution of the possible deviations from the steady-state condition is estimated by minimizing Pearson's ϰ2 subject to the mean fluctuations available. The optimum Pearson function ϰ* may be interpreted as the wave function of the system and in the case of the harmonic oscillator, the free particle in a box, and the hydrogen atom, the prediction based on it is compatible with that provided by the solution of the corresponding Schrödinger equations.

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Guiasu, S. Deducing the Schrödinger equation from minimum χ2 . Int J Theor Phys 31, 1153–1176 (1992).

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  • Hydrogen
  • Wave Function
  • Probability Distribution
  • Field Theory
  • Hydrogen Atom