Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

The Particle in a Box

Description

This lecture covers the concept of the particle in a box, discussing the wave function, energy levels, and solutions in different regions. It also explores the conditions for continuity and analyticity of the wave function.

Official source

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.

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).

Particle

In the physical sciences, a particle (or corpuscule in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from subatomic particles like the electron, to microscopic particles like atoms and molecules, to macroscopic particles like powders and other granular materials. Particles can also be used to create scientific models of even larger objects depending on their density, such as humans moving in a crowd or celestial bodies in motion.

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.

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.

Related lectures (31)

Quantum Mechanics: Principles and Wave Functions

Explores quantum mechanics principles, wave functions, energy quantization, and particle confinement in a box.

Quantum Mechanics: Probability in Potential Wells

Delves into quantum mechanics, focusing on probability in potential wells and comparing classical and quantum predictions.

The Coulomb Potential

Covers the Coulomb potential, magnetic energy, angular momentum, and quantum mechanics concepts.

Advanced General Chemistry I: Quantum Mechanics Principles

Introduces the principles of quantum mechanics, focusing on particle confinement and energy quantization.

Advanced General Chemistry I