The nuclear spin response to a rotating field H has been theoretically investigated from the 1930s to the 1950s. Building upon Majorana's probability theory, the behavior of spin 1/2 is well-illustrated in the joint review by Rabi, Ramsey, andSchwinger, and their spin wave function ψ is succinctly restated by Gottfried: ψ(t) = e-iIzωt/ℏe-i[Iz(ω0-ω)+Ixω1]t/ℏψ(0).
However, the complexity involved in evaluating the wave function ψ in terms of probability amplitudes Cm attributed to the noncommutative nature of spin operators [Ix, Iz] ≠0, hinders the application of this well-established theory to spins with arbitrary values I > 1/2. In a recent study by Hall and Klemm, a conjectural form of the spin wave function was suggested.
Here, we present an alternative formulation of the wave function ψ by controlling doubly rotating coordinates: ψ(t) = e-iIzωt/ℏ e-iIyθ/ℏ e-iIzΩt/ℏ eiIyθ/ℏ ψ(0). This formulation facilitates the computation of general state transitions from an initial state ψ(0)=∑mCm(0)ψm(0) to ψ(t)=∑m'Cm'(t)ψm'(t). Moreover, by assuming an analogous form of the total electron spin J to that of the nucleus I, we can explore hyperfine structures in atoms and/or molecules traversing in the magnetic field H in terms of the nuclear-electronic spin interaction (I·J).
Through this approach, we not only formulate wave functions more effectively but also bridge quantum mechanics and algebraic perspectives.
| Identifer | oai:union.ndltd.org:ucf.edu/oai:stars.library.ucf.edu:etd2023-1173 |
| Date | 01 January 2024 |
| Creators | Kim, Sunghyun |
| Publisher | STARS |
| Source Sets | University of Central Florida |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Graduate Thesis and Dissertation 2023-2024 |
| Rights | In copyright |
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