Quantum Mechanics of Magnetic Moments in External Fields

Oscar Wallace Greenberg

Halqem Nizamidin, Abduwali Anwar, Sayipjamal Dulat A +1 more

We study the noncommutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric qaudrupole moment, in the presence of an external magnetic field. First, by introducing a shift for the magnetic field, we give the Schrödinger equations in the presence of an external magnetic field both on a noncommutative space and a noncommutative phase space, respectively. Then by solving the Schrödinger equations both on a noncommutative space and a noncommutative phase space, we obtain quantum phases of the electric quadrupole moment, respectively. We demonstrate that these phases are geometric and dispersive.

Enrico Fermi

Ali Soltanmanesh, Mahboobe Sehati, Sareh Rostami +2 more

Radical pairs induced by light-driven reduction of cryptochrome protein constitute a spin dependent mechanism that is accompanied by an electric dipole moment and is found to be sensitive to external magnetic fields. In this research, to investigate for the further proof of such model, the simultaneous effect of the Earth's static magnetic field and the time-dependent magnetic field noise on the electric dipole moment of the radical pair has been studied within the quantum mechanical framework. The effect of the external magnetic field discussed in different angles regarding the Earth magnetic field within various frequencies and magnitudes. The sensitivity of the system behavior to the external magnetic field frequencies and magnitudes, vastly differs among the changes in the magnetic field angle to the Earth's static field. Furthermore, the sensitivity studied under the effect of the environmental noise. The relative spatial orientation of the two magnetic field components plays an important role in the time evolution of the electric dipole moment. Also, deeper discussions on specific relative orientations of the external magnetic fields, such as 24 degree, shows that the quantum model of radical pairs which is based on dipole moment, is in agreement with the results of the birds behavorial studies. These findings provide new insights into the sensitivity of the radical pair model to the combination of magnetic fields and may contribute to a comprehensive understanding of the phenomenon of magnetoreception and the advancement of bioinspired magnetic sensors.

Daniel Thies

Randall B. Stafford, Michel Louis Lauzon, Mohammad Sabati +2 more

The purpose of this tutorial is to derive the precessional characteristics of the magnetic moments of hydrogen nuclei in the presence of a constant external magnetic field using the Dirac bra-ket formulation of quantum mechanics (QM). This behaviour has many applications, most notably in nuclear magnetic resonance (NMR) and magnetic resonance (MR) imaging. Many NMR and MR imaging textbooks claim that the QM expectation value of the magnetic moment of a proton in a magnetic field reduces to the classical picture of a precessing magnetic dipole. This paper validates this conclusion by reducing the cumbersome QM integrals using Dirac notation and matrix algebra, and then comparing this result with the classical picture. It illustrates the connections between the quantum and classical pictures and demonstrates quantitatively how they differ and how they are similar. This tutorial targets students and researchers interested in the fundamental physics behind the MR phenomenon and assumes that the reader has a basic understanding of QM. This may be helpful for undergraduate QM students learning about spin angular momentum and Dirac notation.