Proton wave function in a water molecule: Breakdown of degeneration caused by interactions with the magnetic field of a Magnetic Resonance Imaging device

Cristian Heber Zepeda Fernández; Jorge Luis Aguilar Cuevas; Eduardo Moreno Barbosa

doi:10.31349/RevMexFis.68.031101

Authors

Cristian Heber Zepeda Fernández CONACyT, FCFM-BUAP
Jorge Luis Aguilar Cuevas
Eduardo Moreno Barbosa

DOI:

https://doi.org/10.31349/RevMexFis.68.031101

Keywords:

Magnetic resonance imaging, water molecule, energy levels, quantum mechanics

Abstract

The concept of a Magnetic Resonance Imaging (MRI) device is based on the emission of radio waves produced by the protons of the hydrogen atoms in water molecules when placed in a constant magnetic field after they interact with a pulsed radio frequency (RF) current. When the RF field is turned on, the protons are brought to a spin excited state. When the RF field is turned off, the MRI sensors are able to detect the energy released as the protons realign their spins with the magnetic field. In this work we provide a simple model to describe the basic physical mechanism responsible for the operation of MRI devices. We model the water molecule in terms of a central force problem, where the protons move around the (unstructured) doubly negatively charged oxygen atom. First, we employ an analytical treatment to obtain the system's wave function as well as its energy levels, which we show are degenerate. Next, the energy levels from the water molecule are studied in the presence of a uniform external magnetic field. As a result, they get shifted and the degeneration is lifted. We provide numerical results for a magnetic field strength commonly used in MRI devices.

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