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Lecture

Principles of Quantum Mechanics: Harmonic Oscillator

In course

CH-110: Advanced general chemistry I

Le cours comporte deux parties. Les bases de la thermodynamique des équilibres et de la cinétique des réactions sont introduites dans l'une d'elles. Les premières notions de chimie quantique sur les électrons et les liaisons chimiques, exemplifiées en chim ...

Description

This lecture covers the principles of quantum mechanics, focusing on the harmonic oscillator. It explains the probability density distribution in a particle box, the concept of expectation value, and the operators used in quantum mechanics. The Schrödinger equation is introduced to find the wave function and energy of a system.

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Instructors (7)

Marinella Mazzanti

Philippe Schwaller

Anne-Clémence Corminboeuf

Beat Fierz

Jacques-Edouard Moser

Jacques-Edouard Moser is titular professor in physical chemistry and is currently directing the Group for Photochemical Dynamics (Moser Group) of EPFL. He is a graduate of the École polytechnique fédérale de Lausanne, where he received a diploma degree (MSc) in chemical engineering in 1982. After two stays in 1984 and 1985 at Concordia University in Montréal (Canada), he earned in 1986 his Ph.D. in physical chemistry at EPFL (Michael Grätzel, thesis advisor). In 1986, he joined the Eastman Kodak Corporate Research Laboratories at Rochester (NY, USA) as a postdoctoral fellow and was later associated with the NSF Center for Photoinduced Electron Transfer at the University of Rochester. Returning to Switzerland, he was appointed as a lecturer of physical chemistry at EPFL in 1992 and was awarded the habilitation and the venia legendi in 1998. He is titular professor since 2005.His research activity focuses on the study of the dynamics of photoinduced electron transfer and charge carrier separation at donor-acceptor heterojunctions and in nanostructured semiconductors. He is the author and co-author of ca 200 scientific papers (H-index 75). He currently teaches general physical chemistry to freshmen students in chemistry. He gives two classes on general- and redox photochemistry in the MSc program in chemistry and chemical engineering and the doctoral programs in energy and photonics. Jacques-E. Moser presided the Swiss Society of Photochemistry and Photophysics (1995-1998) and chaired the jury of the Grammaticakis-Neumann international prize in photochemistry (1999-2001). He was a member of the board of the Swiss Chemical Society (2007-2012). He served as a member of the standing committee of the European Photochemistry Association (1992-2000) and of the executive committee of the division for fundamental research of the Swiss Chemical Society (1999-2014). He was the director of the Section of Chemistry and Chemical Engineering of EPFL and a member of the direction of the School of Basic Sciences from 2007 to 2015.

Jérôme Waser

Jérôme Waser biography and CV's are available on the following website: http://lcso.epfl.ch/waser

Official source

Ontological neighbourhood

Physics

Quantum mechanics: Mathematical formulation of quantum mechanics

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.

Wave function

In quantum physics, a wave function (or wavefunction), represented by the Greek letter Ψ, is a mathematical description of the quantum state of an isolated quantum system. In the Copenhagen interpretation of quantum mechanics, the wave function is a complex-valued probability amplitude; the probabilities for the possible results of the measurements made on a measured system can be derived from the wave function. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively).

Operator (physics)

In physics, an operator is a function over a space of physical states onto another space of physical states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group useful in this context). Because of this, they are useful tools in classical mechanics. Operators are even more important in quantum mechanics, where they form an intrinsic part of the formulation of the theory.

Schrödinger equation

The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. The equation is named after Erwin Schrödinger, who postulated the equation in 1925 and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933. Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics.

Creation and annihilation operators

Creation operators and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. An annihilation operator (usually denoted ) lowers the number of particles in a given state by one. A creation operator (usually denoted ) increases the number of particles in a given state by one, and it is the adjoint of the annihilation operator.

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