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Non-Hermitian Quantum Mechanics

Jones-Smith, Katherine A.

Abstract Details

2010, Doctor of Philosophy, Case Western Reserve University, Physics.
The basic structure of quantum mechanics was delineated in the early days of the theory and has not been modified since. One of the fundamental assumptions used in formulating the theory is that operators are represented by Hermitian matrices. In recent years it has been shown that quantum mechanics can be formulated consistently without making this assumption, using instead a combination of the parity (P) and time-reversal (T) operators and a number of other requirements related to P and T. Only the case of even T has been analyzed in the literature; here we generalize the principles to include odd time-reversal. We use this generalization to construct a non-Hermitian version of the Dirac equation, and in doing so discover a new type of particle not allowed within the (Hermitian) Standard Model. Finally we present a potential application of the ideas of non-Hermitian quantum mechanics to the unsolved problems of quantum magnetism and high temperature superconductivity.
Dr. Harsh Mathur, PhD (Advisor)
Idit Zehavi, PhD (Committee Member)
Phil Taylor, PhD (Committee Member)
Tanmay Vachaspati, PhD (Committee Member)
122 p.

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Citations

  • Jones-Smith, K. A. (2010). Non-Hermitian Quantum Mechanics [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1270231293

    APA Style (7th edition)

  • Jones-Smith, Katherine. Non-Hermitian Quantum Mechanics. 2010. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1270231293.

    MLA Style (8th edition)

  • Jones-Smith, Katherine. "Non-Hermitian Quantum Mechanics." Doctoral dissertation, Case Western Reserve University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=case1270231293

    Chicago Manual of Style (17th edition)