Quantum Physics: Orbital Angular Momentum

This lecture introduces the concept of orbital angular momentum in quantum physics, focusing on the mathematical details of finding the eigenfunctions in spherical coordinates. The instructor demonstrates the determination of Legendre functions associated with spherical harmonics, emphasizing their normalization conditions and orthogonality. The lecture explores the significance of spherical harmonics in various applications, such as electromagnetism, showcasing their role in decomposing functions in three dimensions. The discussion concludes with a visual representation of spherical harmonics and highlights the restrictions on the values of L and M. The instructor provides insights into the complexity and conceptual importance of understanding orbital angular momentum in quantum physics.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related lectures (46)

Related concepts (32)

PHYS-313: Quantum physics I

The objective of this course is to familiarize the student with the concepts, methods and consequences of quantum physics.

Electromagnetism

In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electrostatics and magnetism, two distinct but closely intertwined phenomena.

Electromagnetic tensor

In electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in spacetime. The field tensor was first used after the four-dimensional tensor formulation of special relativity was introduced by Hermann Minkowski. The tensor allows related physical laws to be written very concisely, and allows for the quantization of the electromagnetic field by Lagrangian formulation described below.

Electromagnetic field

An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by moving electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical counterpart to the quantized electromagnetic field tensor in quantum electrodynamics (a quantum field theory). The electromagnetic field propagates at the speed of light (in fact, this field can be identified as light) and interacts with charges and currents.

Legendre polynomials

In mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a vast number of mathematical properties and numerous applications. They can be defined in many ways, and the various definitions highlight different aspects as well as suggest generalizations and connections to different mathematical structures and physical and numerical applications. Closely related to the Legendre polynomials are associated Legendre polynomials, Legendre functions, Legendre functions of the second kind, and associated Legendre functions.

Classical electromagnetism

Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model; It is, therefore, a classical field theory. The theory provides a description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible. For small distances and low field strengths, such interactions are better described by quantum electrodynamics, which is a quantum field theory.

Spherical Harmonics PHYS-313: Quantum physics I

Explores spherical harmonics, discussing their mathematical properties and significance in quantum mechanics.

Quantum Physics I PHYS-313: Quantum physics I

Explores eigenvalues, ladder operations, and quantum number values in quantum physics.

Quantum Physics I PHYS-313: Quantum physics I

Explores angular momentum, rotation theory, and spherical harmonics in 3D quantum systems.

Physics Wonders

Explores captivating physics experiments, from rotating systems to sound waves and electromagnetism, demonstrating fundamental concepts in an engaging way.

Physics Demonstrations: Mechanics and Fluid Dynamics

Demonstrates physics experiments on mechanics, fluid dynamics, sound waves, and materials properties.