Lecture

Quantum Mechanics: Principles and Wave Functions

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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 Schrödinger equation, wave functions, and the total energy operator. It explains the importance of the wave function in determining the most probable values of observables. The lecture also delves into the concept of particles confined in a box, discussing energy quantization, edge conditions, and graphical representations of solutions. Additionally, it explores the implications of heavy particles having lower energy levels compared to light particles and the quantification of possible energies. The instructor demonstrates the application of the Schrödinger equation in determining energy levels and the behavior of particles in different spatial dimensions.

Instructors (7)

Angela Steinauer

Since 2022: Head of the Laboratory of Biomolecular Engineering and Nanomedicine (LIBN), EPFL (Switzerland)2019-2021: MSCA Postdoctoral Fellow at ETHZ (Switzerland)2018: Ph.D. in Chemical Biology from Yale University (USA)2007-2012: B.Sc. & M.Sc. in Chemistry from University of Zurich (Switzerland) Teaching & PhD PhD Students Diogo Miguel De Abreu Viegas, Georges Barnikol, Oliver Dennis, Andrea Elizabeth Melgar Aguilar, Paula Oeser, Manutsawee Thanaburakorn Courses Advanced general chemistry I CH

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.

Official source

Ontological neighbourhood

Physics

Quantum mechanics: Mathematical formulation of quantum mechanics

Related concepts (32)

Particle in a box

In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example, a particle trapped inside a large box can move at any speed within the box and it is no more likely to be found at one position than another.

Energy level

A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The term is commonly used for the energy levels of the electrons in atoms, ions, or molecules, which are bound by the electric field of the nucleus, but can also refer to energy levels of nuclei or vibrational or rotational energy levels in molecules.

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.

Energy operator

In quantum mechanics, energy is defined in terms of the energy operator, acting on the wave function of the system as a consequence of time translation symmetry. It is given by: It acts on the wave function (the probability amplitude for different configurations of the system) The energy operator corresponds to the full energy of a system. The Schrödinger equation describes the space- and time-dependence of the slow changing (non-relativistic) wave function of a quantum system.

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).

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