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Applications of integral transform methods to the Schroedinger equation and dynamical systems
Huang, Min

2010, Doctor of Philosophy, Ohio State University, Mathematics.

Integral transform methods, in particular the generalized Borel summation methods, have been employed in the study of ordinary and partial differential equations, difference equations, and dynamical systems. These methods are especially useful for analyzing long time asymptotic behaviors of physical systems, and for describing highly complicated behaviors of dynamical systems.


In the first part of the dissertation we consider one dimensional Schrödinger equations with (1) time-dependent damped delta potentials, (2) time-periodic delta potentials, and (3) time-independent compactly supported (finite-range) potentials. We obtain time-asymptotic expressions for the wave functions, and address several issues of physical interest, including ionization and resonance.


In the second part of the dissertation we study certain types of lacunary series and obtain asymptotic formulas that describe the behaviors of such series at the natural boundary (a barrier of singularities). We then explore the connection between certain special lacunary series and Julia sets.

Ovidiu Costin (Committee Chair)
Saleh Tanveer (Committee Member)
Rodica Costin (Committee Member)

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Huang, M. (2010). Applications of integral transform methods to the Schroedinger equation and dynamical systems. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Huang, Min. "Applications of integral transform methods to the Schroedinger equation and dynamical systems." Electronic Thesis or Dissertation. Ohio State University, 2010. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Huang, Min "Applications of integral transform methods to the Schroedinger equation and dynamical systems." Electronic Thesis or Dissertation. Ohio State University, 2010. https://etd.ohiolink.edu/

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