Physicists in quantum mechanics often refer to momentum rather than velocity because momentum has a more fundamental and well-defined meaning in the context of quantum theory. Velocity, on the other hand, can be a more ambiguous concept when dealing with quantum particles.
In classical physics, velocity is the rate of change of an object's position with respect to time. It is a vector quantity that includes both magnitude (speed) and direction. However, in quantum mechanics, the position and momentum of a particle are described by mathematical entities called operators, which have properties distinct from classical variables.
The momentum operator, denoted by "p," is a fundamental operator in quantum mechanics that acts on a particle's wavefunction. The eigenvalues (possible outcomes) of the momentum operator correspond to the possible values of the particle's momentum. The square of the momentum operator is related to the kinetic energy operator, providing a link between momentum and energy.
In contrast, velocity is not an operator in quantum mechanics. It is not associated with an observable quantity that can be directly measured. Instead, velocity is related to momentum through the concept of group velocity, which is the velocity of a wave packet composed of various momentum components. However, group velocity is not applicable to individual particles or well-defined states.
Furthermore, the uncertainty principle, a fundamental principle in quantum mechanics, states that there is a fundamental limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known. This principle implies that both position and momentum cannot be precisely determined at the same time for a quantum particle.
By focusing on momentum rather than velocity, physicists can work with a quantity that has a clearer mathematical representation in quantum mechanics and is directly related to observables and measurable quantities. Momentum is also closely connected to the wave properties of particles and is more amenable to analysis and calculations in quantum theory.