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Lecture

Quantum Particle in Potential Well

In course

PHYS-207(c): General physics : quanta

Le cours traite les ondes électromagnétiques (optique géométrique et optique physique) et donne une introduction à la physique quantique. ...

Description

This lecture focuses on solving the first question of exercise 23, involving a quantum particle of mass M in a one-dimensional space subjected to a potential well. The width of the potential well is considered along with the wave function for the ground state. The goal is to determine the energy associated with this wave function by specializing the equation for x greater than L/2, resulting in the desired energy value.

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Instructor

Alfredo Pasquarello

Alfredo Pasquarello studied physics at the Scuola Normale Superiore of Pisa and at the University of Pisa, obtaining their respective degrees in 1986. He obtained a doctoral degree at the EPFL in 1991 with a thesis on Multiphoton Transitions in Solids . Then, he moved to Bell Laboratories at Murray Hill (New Jersey), where he carried out postdoctoral research on the magnetic properties of carbon fullerenes. In 1993, he joined the Institute for Numerical Research in the Physics of Materials (IRRMA), where his activity involved first-principles simulation methods. In 1998, he was awarded the EPFL Latsis Prize for his research work on disordered silica materials. Succeeding in grant programs of the Swiss National Science Foundation, he then set up his own research group at IRRMA. In July 2003, he is appointed Professor in Theoretical Condensed Matter Physics at EPFL. Currently, he leads the Chair of Atomic Scale Simulation.

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Related concepts (27)

Three-dimensional space

In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point. Most commonly, it is the three-dimensional Euclidean space, the Euclidean n-space of dimension n=3 that models physical space. More general three-dimensional spaces are called 3-manifolds. Technically, a tuple of n numbers can be understood as the Cartesian coordinates of a location in a n-dimensional Euclidean space.

One-dimensional space

In physics and mathematics, a sequence of n numbers can specify a location in n-dimensional space. When n = 1, the set of all such locations is called a one-dimensional space. An example of a one-dimensional space is the number line, where the position of each point on it can be described by a single number. In algebraic geometry there are several structures that are technically one-dimensional spaces but referred to in other terms. A field k is a one-dimensional vector space over itself.

Energy transition

An energy transition (or energy system transformation) is a significant structural change in an energy system regarding supply and consumption. Currently, a transition to sustainable energy (mostly renewable energy) is underway to limit climate change. It is also called renewable energy transition. The current transition is driven by a recognition that global greenhouse-gas emissions must be drastically reduced. This process involves phasing-down fossil fuels and re-developing whole systems to operate on low carbon electricity.

Primary energy

Primary energy (PE) is the energy found in nature that has not been subjected to any human engineered conversion process. It encompasses energy contained in raw fuels and other forms of energy, including waste, received as input to a system. Primary energy can be non-renewable or renewable. Primary energy is used in energy statistics in the compilation of energy balances, as well as in the field of energetics. In energetics, a primary energy source (PES) refers to the energy forms required by the energy sector to generate the supply of energy carriers used by human society.

Four-dimensional space

Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world. For example, the volume of a rectangular box is found by measuring and multiplying its length, width, and height (often labeled x, y, and z).

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