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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.
Taking the "box" to be a black body cavity, the photons are continually being absorbed and re-emitted by the walls. When this is the case, the number of photons is not conserved. In the derivation of Bose–Einstein statistics , when the restraint on the number of particles is removed, this is effectively the same as setting the chemical ...
Some trajectories of a particle in a box according to Newton's laws of classical mechanics (A), and matter waves (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 wavefunction .
In quantum mechanics, the case of a particle in a one-dimensional ring is similar to the particle in a box. The particle follows the path of a semicircle from 0 {\displaystyle 0} to π {\displaystyle \pi } where it cannot escape, because the potential from π {\displaystyle \pi } to 2 π {\displaystyle 2\pi } is infinite.
1.1 Free spin-0 particle. ... For a particle in a box, ... Download as PDF; Printable version; In other projects Wikidata item Part of a series of articles about ...
Let n denote a complete set of (discrete) quantum numbers for specifying single-particle states (for example, for the particle in a box problem, take n to be the quantized wave vector of the wavefunction.) For simplicity, consider a system composed of two particles that are not interacting with each other.