Lecture

Isolated Magnetic Moments: An Atom In Magnetic Field

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In course

PHYS-491: Magnetism in materials

The lectures will provide an introduction to magnetism in materials, covering fundamentals of spin and orbital degrees of freedom, interactions between moments and some typical ordering patterns. Selected experimental techniques and their application in cu ...

Description

This lecture focuses on deriving the Hamiltonian of an atom in a magnetic field, exploring the paramagnetic and diamagnetic responses. The instructor explains how the canonical momentum influences the base Hamiltonian, considering the kinetic energy and the impact of applying a magnetic field on the canonical momentum. By taking into account the negatively charged electron and the choice of gauge, the final solution is obtained, consisting of the initial Hamiltonian with paramagnetic and diamagnetic contributions.

Instructor

Ivica Zivkovic

Teaching & PhD PhD Students Berna Esmer Past EPFL PhD Students as codirector Virgile Favre, Bhushan Hegde, Yikai Yang Courses Magnetism in materials PHYS-491 The lectures will provide an introduction to magnetism in materials, covering fundamentals of spin and orbital degrees of freedom, interactions between moments and some typical ordering patterns. Selected experimental techniques and their application in current research will be presented.

Official source

Ontological neighbourhood

Physics

Mechanics: Classical mechanics

Related concepts (32)

Scalar potential

In mathematical physics, scalar potential, simply stated, describes the situation where the difference in the potential energies of an object in two different positions depends only on the positions, not upon the path taken by the object in traveling from one position to the other. It is a scalar field in three-space: a directionless value (scalar) that depends only on its location. A familiar example is potential energy due to gravity.

Magnetic vector potential

In classical electromagnetism, magnetic vector potential (often called A) is the vector quantity defined so that its curl is equal to the magnetic field: . Together with the electric potential φ, the magnetic vector potential can be used to specify the electric field E as well. Therefore, many equations of electromagnetism can be written either in terms of the fields E and B, or equivalently in terms of the potentials φ and A. In more advanced theories such as quantum mechanics, most equations use potentials rather than fields.

Electric potential

The electric potential (also called the electric field potential, potential drop, the electrostatic potential) is defined as the amount of work energy needed per unit of electric charge to move this charge from a reference point to the specific point in an electric field. More precisely, it is the energy per unit charge for a test charge that is so small that the disturbance of the field under consideration is negligible.

Canonical coordinates

In mathematics and classical mechanics, canonical coordinates are sets of coordinates on phase space which can be used to describe a physical system at any given point in time. Canonical coordinates are used in the Hamiltonian formulation of classical mechanics. A closely related concept also appears in quantum mechanics; see the Stone–von Neumann theorem and canonical commutation relations for details.

Angular momentum

In physics, angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity – the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. Bicycles and motorcycles, flying discs, rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum.

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