Lecture

Quantum Mechanics: Wave Functions

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In course

PHYS-425: Quantum physics III

To introduce several advanced topics in quantum physics, including semiclassical approximation, path integral, scattering theory, and relativistic quantum mechanics ...

Description

This lecture covers the discussion and construction of wave functions, the De Broglie wavelength, and the classically allowed and forbidden regions. It also delves into the matching conditions at turning points and the Bohr-Sommerfeld quantization. The applicability of the results is explored through examples.

Instructor

Oleg Yazyev

Prof. Oleg Yazyev (Олег Язев) was born in Simferopol, Crimean peninsula. He obtained his degree in chemistry from Moscow State University in 2003. He then joined Ecole Polytechnique Fédérale de Lausanne (EPFL) completing his PhD thesis in chemistry and chemical engineering in 2007. Next two years he has spent as a postdoctoral fellow at the Institute of Theoretical Physics (ITP) and the Institute for Numerical Research in the Physics of Materials (IRRMA) of the same institution. In 2009-2011 he was a postdoctoral fellow at the Department of Physics of the University of California, Berkeley and the Lawrence Berkeley National Laboratory. In September 2011 he started an independent research group supported by the Swiss National Science Foundation professorship grant. In 2012 he was awarded an ERC Starting grant. His current research focuses on theoretical and computational physics of two-dimensional and topological materials with strong emphasis on their prospective technological applications. ResearcherID profile of Oleg Yazyev Google Scholar profile of Oleg Yazyev

Official source

Related concepts (32)

Lecture

A lecture (from lēctūra ) is an oral presentation intended to present information or teach people about a particular subject, for example by a university or college teacher. Lectures are used to convey critical information, history, background, theories, and equations. A politician's speech, a minister's sermon, or even a business person's sales presentation may be similar in form to a lecture. Usually the lecturer will stand at the front of the room and recite information relevant to the lecture's content.

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.

Bohr model

In atomic physics, the Bohr model or Rutherford–Bohr model of the atom, presented by Niels Bohr and Ernest Rutherford in 1913, consists of a small, dense nucleus surrounded by orbiting electrons. It is analogous to the structure of the Solar System, but with attraction provided by electrostatic force rather than gravity, and with the electron energies quantized (assuming only discrete values).

Old quantum theory

The old quantum theory is a collection of results from the years 1900–1925 which predate modern quantum mechanics. The theory was never complete or self-consistent, but was rather a set of heuristic corrections to classical mechanics. The theory is now understood as the semi-classical approximation to modern quantum mechanics. The main and final accomplishments of the old quantum theory were the determination of the modern form of the periodic table by Edmund Stoner and the Pauli Exclusion Principle which were both premised on the Arnold Sommerfeld enhancements to the Bohr model of the atom.

WKB approximation

In mathematical physics, the WKB approximation or WKB method is a method for finding approximate solutions to linear differential equations with spatially varying coefficients. It is typically used for a semiclassical calculation in quantum mechanics in which the wavefunction is recast as an exponential function, semiclassically expanded, and then either the amplitude or the phase is taken to be changing slowly. The name is an initialism for Wentzel–Kramers–Brillouin. It is also known as the LG or Liouville–Green method.

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