Complex Numbers in Quantum Theory

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In 1927, Nobel prize winning physicist, E. Schrodinger, in correspondence with Ehrenfest, wrote the following about the new theory: “What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. Psi is surely fundamentally a real function.” This seemingly simple issue remains unexplained almost ninety years later. In this dissertation I elucidate the physical and theoretical origins of the complex requirement. I identify a freedom/constraint situation encountered by vectors when, employed in accordance with adopted quantum representational methodology, and representing angular momentum states in particular. Complex vectors, quite simply, provide more available adjustable variables ... continued below

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v, 38 pages : color illustrations

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Maynard, Glenn August 2015.

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This dissertation is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 69 times , with 7 in the last month . More information about this dissertation can be viewed below.

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  • Maynard, Glenn

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In 1927, Nobel prize winning physicist, E. Schrodinger, in correspondence with Ehrenfest, wrote the following about the new theory: “What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. Psi is surely fundamentally a real function.” This seemingly simple issue remains unexplained almost ninety years later. In this dissertation I elucidate the physical and theoretical origins of the complex requirement. I identify a freedom/constraint situation encountered by vectors when, employed in accordance with adopted quantum representational methodology, and representing angular momentum states in particular. Complex vectors, quite simply, provide more available adjustable variables than do real vectors. The additional variables relax the constraint situation allowing the theory’s representational program to carry through. This complex number issue, which lies at the deepest foundations of the theory, has implications for important issues located higher in the theory. For example, any unification of the classical and quantum accounts of the settled order of nature, will rest squarely on our ability to account for the introduction of the imaginary unit.

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v, 38 pages : color illustrations

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UNT Theses and Dissertations

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  • August 2015

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  • March 4, 2016, 4:14 p.m.

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  • May 12, 2017, 6:53 a.m.

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Maynard, Glenn. Complex Numbers in Quantum Theory, dissertation, August 2015; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc804988/: accessed December 11, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .