**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# Separation of Variables

Description

This lecture covers the concept of separation of variables in the context of quantum mechanics, focusing on the mathematical techniques used to solve differential equations. The instructor discusses the application of this method in various physical systems and its significance in simplifying complex problems.

Official source

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.

In course

Instructor

CH-244: Quantum chemistry

Introduction to Quantum Mechanics with examples related to chemistry

Related concepts (237)

2

2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures. The digit used in the modern Western world to represent the number 2 traces its roots back to the Indic Brahmic script, where "2" was written as two horizontal lines. The modern Chinese and Japanese languages (and Korean Hanja) still use this method.

Lie algebra

In mathematics, a Lie algebra (pronounced liː ) is a vector space together with an operation called the Lie bracket, an alternating bilinear map , that satisfies the Jacobi identity. Otherwise said, a Lie algebra is an algebra over a field where the multiplication operation is now called Lie bracket and has two additional properties: it is alternating and satisfies the Jacobi identity. The Lie bracket of two vectors and is denoted . The Lie bracket does not need to be associative, meaning that the Lie algebra can be non associative.

Lie group

In mathematics, a Lie group (pronounced liː ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additional properties it must have to be thought of as a "transformation" in the abstract sense, for instance multiplication and the taking of inverses (division), or equivalently, the concept of addition and the taking of inverses (subtraction).

1

1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0.

H

H, or h, is the eighth letter in the Latin alphabet, used in the modern English alphabet, including the alphabets of other western European languages and others worldwide. Its name in English is aitch (pronounced eɪtʃ, plural aitches), or regionally haitch heɪtʃ. The original Semitic letter Heth most likely represented the voiceless pharyngeal fricative (ħ). The form of the letter probably stood for a fence or posts. The Greek Eta 'Η' in archaic Greek alphabets, before coming to represent a long vowel, /ɛː/, still represented a similar sound, the voiceless glottal fricative /h/.

Related lectures (1,000)

Quantum Chemistry: Energy Quantization and EigenvaluesCH-343: Spectroscopy

Covers the quantization of energy levels in quantum chemistry.

Quantum Mechanics: Power Series SolutionsCH-244: Quantum chemistry

Explores power series solutions in quantum mechanics for differential equations and energy quantization.

Quantum Mechanics: BasicsCH-244: Quantum chemistry

Introduces the basics of quantum mechanics, covering wave functions, operators, and the uncertainty principle.

Measurement of Observable EigenvaluesCH-244: Quantum chemistry

Covers the measurement of observable eigenvalues and the importance of complete orthonormal sets.

Understanding Chaos in Quantum Field Theories

Explores chaos in quantum field theories, focusing on conformal symmetry, OPE coefficients, and random matrix universality.