Free particle

In physics, a free particle is a particle that, in some sense, is not bound by an external force, or equivalently not in a region where its potential energy varies. In classical physics, this means the particle is present in a 'field-free' space. In quantum mechanics, it means a region of uniform potential, usually set to zero in the region of interest since potential can be arbitrarily set to zero at any point (or surface in three dimensions) in space. In physics, a free particle is a particle that, in some sense, is not bound by an external force, or equivalently not in a region where its potential energy varies. In classical physics, this means the particle is present in a 'field-free' space. In quantum mechanics, it means a region of uniform potential, usually set to zero in the region of interest since potential can be arbitrarily set to zero at any point (or surface in three dimensions) in space. The classical free particle is characterized by a fixed velocity v. The momentum is given by and the kinetic energy (equal to total energy) by where m is the mass of the particle and v is the vector velocity of the particle. A free particle in non-relativistic quantum mechanics is described by the free Schrödinger equation: where ψ is the wavefunction of the particle at position r and time t. The solution for a particle with momentum p or wave vector k, at angular frequency ω or energy E, is given by the complex plane wave: with amplitude A. The eigenvalue spectrum is infinitely degenerate since for each eigenvalue E>0, there corresponds an infinite number of eigenfunctions corresponding to different directions of p {displaystyle mathbf {p} } . As for all quantum particles free or bound, the Heisenberg uncertainty principles (similarly for the y and z directions), and the De Broglie relations: apply. Since the potential energy is (set to) zero, the total energy E is equal to the kinetic energy, which has the same form as in classical physics: