Lecture

Quantum Mechanics: Wavefunctions and Operators

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In course

MSE-486: Organic electronic materials

This course will introduce students to the field of organic electronic materials. The goal of this course is to discuss the origin of electronic properties in organic materials, charge transport mechanisms, chemical synthesis, materials processing, and dev ...

Description

This lecture covers the fundamentals of quantum mechanics, focusing on wave-particle duality, complex wavefunctions, Dirac notation, Hermitian operators, and the Born interpretation. It explains how quantum systems are described, the importance of Hermiticity, and the quantization of particle energies.

Instructor

Holger Frauenrath

Holger Frauenrath (born in Aachen, Germany) studied chemistry at RWTH Aachen , Germany from 1992 to 1997, with a focus on synthetic organic chemistry. He performed his PhD thesis from 1998 to 2001 in the research group of Prof Hartwig Höcker at RWTH Aachen, working on a project related to the stereospecific polymerization of methacrylates as well as their copolymerization with olefins using zirconocene catalysts. Holger Frauenrath then joined the group of Prof. Sam Stupp at Northwestern University , Evanston, IL, USA, as a postdoctoral fellow supported by a Feodor Lynen fellowship of the Alexander von Humboldt Foundation . His postdoctoral research projects were centered around the supramolecular self-assembly of rod-coil molecules. Holger Frauenrath returned to Germany in 2003 and started to build his own research group at FU Berlin, funded with an Emmy Noether Grant from the German Science Foundation . In 2005, the research group moved to the Department of Materials at ETH Zurich , Switzerland, where it became a scientifcally independent part of the Polymer Chemistry Group led by Prof. A. Dieter Schlüter . Holger Frauenrath obtained his Habilitation from ETH Zurich in 2009. In 2009, Holger Frauenrath has been appointed as a professor at the Institute of Materials (IMX) of the Ecole Polytechnique Federale de Lausanne (EPFL) , Switzerland, building the new Laboratory of Macromolecular and Organic Materials (LMOM) . In the same year, Holger Frauenrath was received the prestigious European Research Council (ERC) Starting Investigator grant.

Official source

Related concepts (30)

Interpretations of quantum mechanics

An interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics might correspond to experienced reality. Although quantum mechanics has held up to rigorous and extremely precise tests in an extraordinarily broad range of experiments, there exist a number of contending schools of thought over their interpretation. These views on interpretation differ on such fundamental questions as whether quantum mechanics is deterministic or stochastic, local or non-local, which elements of quantum mechanics can be considered real, and what the nature of measurement is, among other matters.

Copenhagen interpretation

The Copenhagen interpretation is a collection of views about the meaning of quantum mechanics, stemming from the work of Niels Bohr, Werner Heisenberg, Max Born, and others. The term "Copenhagen interpretation" was apparently coined by Heisenberg during the 1950s to refer to ideas developed in the 1925–1927 period, glossing over his disagreements with Bohr. Consequently, there is no definitive historical statement of what the interpretation entails.

Many-worlds interpretation

The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wavefunction is objectively real, and that there is no wave function collapse. This implies that all possible outcomes of quantum measurements are physically realized in some "world" or universe. In contrast to some other interpretations, such as the Copenhagen interpretation, the evolution of reality as a whole in MWI is rigidly deterministic and local.

Ensemble interpretation

The ensemble interpretation of quantum mechanics considers the quantum state description to apply only to an ensemble of similarly prepared systems, rather than supposing that it exhaustively represents an individual physical system. The advocates of the ensemble interpretation of quantum mechanics claim that it is minimalist, making the fewest physical assumptions about the meaning of the standard mathematical formalism. It proposes to take to the fullest extent the statistical interpretation of Max Born, for which he won the Nobel Prize in Physics in 1954.

Wave–particle duality

Wave–particle duality is the concept in quantum mechanics that quantum entities exhibit both particle and a wave properties according to the experimental circumstances. It expresses the inability of the classical concepts "particle" or "wave" to fully describe the behaviour of quantum-scale objects. As Albert Einstein wrote: It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty.

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