Joel Campbell

NASA, Washington, West Virginia, United States

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Publications (3)4.7 Total impact

  • Joel Campbell
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    ABSTRACT: The time-dependent Schrödinger equation with a time-dependent delta function potential is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation of the Volterra type. It is shown that by knowing the wavefunction at the origin, one may derive the wavefunction everywhere. Thus, the problem is reduced from a PDE in two variables to an integral equation in one. These results are used to compare adiabatic versus sudden changes in the potential. It is shown that adiabatic changes in the potential lead to the conservation of the normalization of the probability density.
    Journal of Physics A Mathematical and Theoretical 08/2009; 42(36):365212. · 1.77 Impact Factor
  • Joel Campbell
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    ABSTRACT: A method is developed to demodulate (velocity correct) Fourier transform spectrometer data that are taken with an analog to digital converter that digitizes equally spaced in time. This method makes it possible to use simple low-cost, high-resolution audio digitizers to record high-quality data without the need for an event timer or quadrature laser hardware and makes it possible to use a metrology laser of any wavelength. The reduced parts count and simple implementation make it an attractive alternative in space-based applications when compared to previous methods such as the Brault algorithm.
    Applied Optics 01/2009; 47(36):6889-94. · 1.69 Impact Factor
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    Joel Campbell
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    ABSTRACT: A generalized single-step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.
    Theoretical Population Biology 01/2008; 72(4):539-46. · 1.24 Impact Factor

Publication Stats

5 Citations
4.70 Total Impact Points

Institutions

  • 2008–2009
    • NASA
      Washington, West Virginia, United States