Lecture

Quantum Mechanics: Wave-Particle Duality of Electrons

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In course

MICRO-312: Physics of semiconductors devices

Les étudiants savent expliquer la physique des composants semiconducteurs, tels que diodes, transistors et composants MOS. Ils les utilisent dans des circuits électroniques fondamentaux tels qu'inverseurs et ampli. ...

Description

This lecture discusses the wave-particle duality of electrons, illustrating how quantum mechanics describes particles as both waves and particles. The instructor explains the interactions of electrons with matter, emphasizing their behavior as wave functions characterized by frequency and wave vector. The lecture covers the principles of energy and momentum in quantum mechanics, introducing key relationships such as Planck's relation and the de Broglie hypothesis. The propagation of particles in a vacuum is analyzed, highlighting the concept of wave packets and their oscillatory modes. The instructor demonstrates how to describe wave functions using Fourier transforms and discusses the implications of measuring particle probabilities. The lecture also explores the significance of electron behavior in electron microscopes, detailing how high-energy electrons can achieve high resolution. Finally, the instructor presents simulations to illustrate the propagation of electrons and the differences between phase velocity and group velocity, reinforcing the importance of understanding electron behavior in quantum mechanics.

Instructor

Pierre-André Besse

Teaching & PhD Past EPFL PhD Students Klaus Ehrmann Courses La science quantique : une vision singulière MICRO-444 Students understand the characteristics of quantum science. They master the formalism and use it in basic quantum systems: quantum wells, wires, dots or qubits. Physics of semiconductors devices MICRO-312 The students are able to explain the physics of semiconductor devices like diodes, transistors, and MOS devices. They use such devices in fundamental electroni

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Related concepts (32)

Matter wave

Matter waves are a central part of the theory of quantum mechanics, being half of wave–particle duality. All matter exhibits wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave. The concept that matter behaves like a wave was proposed by French physicist Louis de Broglie (dəˈbrɔɪ) in 1924, and so matter waves are also known as de Broglie waves.

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.

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).

Probability

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin.

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.

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