Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

The Schur Lemma: Physical Interpretation

In course

PHYS-314: Quantum physics II

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

Description

This lecture delves into the group repetition theory, focusing on the Schur lemma and its physical interpretation in quantum physics. The slides cover the direct sum of irreducible representations, orthogonality, and the reduction of matrices. Through examples and mathematical formulations, the instructor explains the significance of the Schur lemma in understanding the behavior of quantum systems.

Instructors (3)

Florent Gérard Krzakala

Zoë Holmes

Vincenzo Savona

Vincenzo Savona studied physics in Pisa at the Scuola Normale Superiore and the University of Pisa, prior to completing his PhD at the EPFL's Institute of Theoretical Physics. Subsequently he did post-doctoral work, first at the EPFL and then in the physics department of the Humboldt University of Berlin. In 2002, he returned to the EPFL to create his own research group, receiving a "professeur boursier" fellowship from the Swiss National Science Foundation. In 2006, he was appointed tenure-track assistant professor at the EPFL and joined the NCCR for Quantum Photonics. In 2010 he was appointed associate professor. Currently he directs the Laboratory of Theoretical Physics of Nanosystems.

Official source

Related concepts (32)

Quantum mechanics

Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales.

Measurement in quantum mechanics

In quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result. A fundamental feature of quantum theory is that the predictions it makes are probabilistic. The procedure for finding a probability involves combining a quantum state, which mathematically describes a quantum system, with a mathematical representation of the measurement to be performed on that system. The formula for this calculation is known as the Born rule.

Philosophy of physics

In philosophy, philosophy of physics deals with conceptual and interpretational issues in modern physics, many of which overlap with research done by certain kinds of theoretical physicists. Philosophy of physics can be broadly divided into three areas: interpretations of quantum mechanics: mainly concerning issues with how to formulate an adequate response to the measurement problem and understand what the theory says about reality.

Mathematical formulation of quantum mechanics

The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space. Such are distinguished from mathematical formalisms for physics theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces (L2 space mainly), and operators on these spaces.

Quantum field theory

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles.

Related lectures (34)

Projectors on Invariant Subspaces

Covers projectors on invariant subspaces in quantum physics and their applications.

Lemma of Schur: Group Repetition Theory

Explores irreducible and reducible representations in group repetition theory and the lemma of Schur in quantum physics.

Group Theory & Quantum Mechanics

Explores k-fold degenerate sets of eigenfunctions and their basis for irreducible representations.

Group Representations Theory Application Overview

Covers the application of group representations theory in quantum physics.

Time-Independent Perturbation Theory: Degenerate Case