Some trajectories of a particle in a box according to Newton's laws of classical mechanics (A), and according to the Schrödinger equation of quantum mechanics (B–F). In (B–F), the horizontal axis is position, and the vertical axis is the real part (blue) and imaginary part (red) of the wave function. The states (B,C,D) are energy eigenstates, but (E,F) are not.
In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes the movement of a free particle 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. However, when the well becomes very narrow (on the scale of a few nanometers), quantum effects become important. The particle may only occupy certain positive energy levels. Likewise, it can never have zero energy, meaning that the particle can never "sit still". Additionally, it is more likely to be found at certain positions than at others, depending on its energy level. The particle may never be detected at certain positions, known as spatial nodes.
The particle in a box model is one of the very few problems in quantum mechanics that can be solved analytically, without approximations. Due to its simplicity, the model allows insight into quantum effects without the need for complicated mathematics. It serves as a simple illustration of how energy quantizations (energy levels), which are found in more complicated quantum systems such as atoms and molecules, come about. It is one of the first quantum mechanics problems taught in undergraduate physics courses, and it is commonly used as an approximation for more complicated quantum systems.
In the physical sciences, aparticle (or corpuscule in older texts) is a small localized object which can be described by several physical or chemical...
In quantum mechanics, the results of the quantum particleinabox can be used to look at the equilibrium situation for a quantum ideal gas inabox which...
illustrating that the particle may be in motion even if its spatial probability density has no explicit time dependence. For aparticleinabox, in one spatial...
In physics, a free particle is aparticle that, in some sense, is not bound by an external force, or equivalently not ina region where its potential energy...
In experimental and applied particle physics, nuclear physics, and nuclear engineering, aparticle detector, also known as a radiation detector, is a...
need not be balanced in general. Consider aparticleina one-dimensional box of length L {\displaystyle L} . The eigenfunctions in position and momentum...
then be modeled using the particleinabox model in which the energy of different states is dependent on the length of the box. The wave functions for...
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in a one-dimensional box is a half-period sine wave, which goes to zero at the two edges of the well. The energy of the particle is given by h 2 n 2 8...
In quantum mechanics, aparticleina spherically symmetric potential is a system with a potential that depends only on the distance between the particle...
that confined carriers can be in are particle-in-a-box-like states. Quantum wells and quantum well devices are a subfield of solid-state physics that...
partition function. Assuming a 1-dimensional box of length L, the partition function (using the energy states of the 1D particleinabox) is Z=∑ne−En/kBT=∑ne−h2n2/8mL2kBT...
square well) is a concept from quantum mechanics. It is an extension of the infinite potential well, in which aparticle is confined to a "box", but one which...
models in physics to simplify things. Massless ropes, point particles, ideal gases and the particleinabox are among the many simplified models used in physics...
Matter waves are a central part of the theory of quantum mechanics, being half of wave–particle duality. At all scales where measurements have been practical...
Aparticle counter is used for monitoring and diagnosing particle contamination within specific clean media, including air, water and chemicals. Particle...
shortens. A rather good approximation of an exciton's behaviour is the 3-D model of aparticleinabox. The solution of this problem provides a sole[clarification...
In quantum mechanics, indistinguishable particles (also called identical or indiscernible particles) are particles that cannot be distinguished from one...
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