Keywords

NMR, EPR, Magnetic Dipole Moment, Electric Quadrupole Moment, Multipole Moments, Lie Group

Abstract

To accurately solve the general nuclear spin state function in Nuclear Magnetic Resonance (NMR), a rotation wave approach was employed, allowing the reference frame to rotate in sync with the oscillating magnetic field. The spin state system was analogously treated as a Rubik's Cube, ensuring the diagonalization of only the time-dependent part of the state function. Although Gottfried's equation (1966) aligns with transitions between specific spin states m and m′, his second rotation contradicts the conservation of angular momentum, resulting in inaccuracies for spin states with initial phase shifts or entangled states. Contrarily, Schwinger (1937) efficiently computed the coefficients for each spin state in a frequency range opposite to the Larmor frequency, using an unorthodox approach in quantum mechanics, which unfortunately led to the oversight of his work in subsequent citations. This methodology was also applied to derive the general electron spin state function in Nuclear Magnetic Resonance (NMR) and Electron Paramagnetic Resonance (EPR), enabling the construction of a doubly rotated ground state for time-dependent perturbation theory. This was particularly relevant as the Hamiltonians for magnetic dipole, electric quadrupole, and magnetic octupole moments incorporate powers of I · J terms, necessitating the calculation of sub-state energy levels for perturbation, including those of molecules 14N7 and 7Li3. Furthermore, the study expanded to the general Lie group for 3D rotations along three linearly independent axes, resulting in 12 distinct methods to achieve rotations in any arbitrary direction using these axes, yielding wave function with only one spin operator in each exponent. The ongoing research is now concentrated on generating NMR spectra for 14N7 in amino acids, furthering the understanding of nuclear spin dynamics in complex molecular systems.

Completion Date

2024

Semester

Spring

Committee Chair

Klemm, Richard

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

Physics

Degree Program

Physics

Format

application/pdf

Identifier

DP0028324

URL

https://purls.library.ucf.edu/go/DP0028324

Language

English

Rights

In copyright

Release Date

May 2024

Length of Campus-only Access

None

Access Status

Doctoral Dissertation (Open Access)

Campus Location

Orlando (Main) Campus

Accessibility Status

Meets minimum standards for ETDs/HUTs

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Physics Commons

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