Consider Maxwell's set-up, but with only a single gas particle in a box.

The simplest form of the particle in a box model considers a one-dimensional system.

This applies to the elementary "particle in a box" problem, and step potentials.

The general solutions of the Schrödinger equation for the particle in a box are:

A rather good approximation of an exciton's behaviour is the 3-D model of a particle in a box.

Then to each possible quantum motion of a particle in a box associate an independent harmonic oscillator.

If the quantum well is very deep, it can be approximated by the particle in a box model, in which .

The particle in a box model provides one of the very few problems in quantum mechanics which can be solved without approximations.

Many upper-division science students are familiar with the particle in a box, or the particle in a ring.

Elementary examples that show mathematically how energy levels come about are the particle in a box and the quantum harmonic oscillator.

The integral is easiest for a particle in a box of length L, where the quantum condition is:

(See also: Particle in a box, Mathematical formulation of quantum mechanics.)

For the particle in a box, it can be shown that the average position is always , regardless of the state of the particle.

Second, these discrete energy levels are equally spaced, unlike in the Bohr model of the atom, or the particle in a box.

Analogous to the wave function of a particle in a box, one finds that the fields are superpositions of periodic functions.

Massless ropes, point particles, ideal gases and the particle in a box are among the many simplified models used in physics.

A simple way to derive this law is to consider an alpha particle in the atomic nucleus as a particle in a box.

In quantum mechanics, the case of a particle in a one-dimensional ring is similar to the particle in a box.

Single-particle states are usually enumerated in terms of their momenta (as in the particle in a box problem.)

These recurrences are imposed as semiclassical quantization conditions, similarly to the quantization of a particle in a box.

We outline the solutions in these cases, which should be compared to their counterparts in cartesian coordinates, cf. particle in a box.

Physicists regularly announce new particles observed in the debris from extremely energetic particle collisions, but you cannot buy one of these new particles in a box.

For a particle in a box (and for a free particle as well), the relationship between energy and momentum is different for massive and massless particles.

The energy levels can then be modeled using the particle in a box model in which the energy of different states is dependent on the length of the box.

Using cylindrical coordinates, the operators and are expressed as and respectively, where these observables play a role similar to position and momentum for the particle in a box.