What is the momentum of a free particle?

For a classical free particle, the linear momentum p =mv is a constant of motion, that is, a quantity that does not change during the motion of the particle. The kinetic energy of the particle E = |p|2/2m = p2/2m (equal to the total energy for a free particle) is also a constant of motion.

Can a free particle be Normalised?

For all we know, a free particle with well-defined energy could be found anywhere in the whole Universe. We say that this quantum state is maximally delocalised, and such states cannot be normalised since the particle has a finite probability to be found at |x|→∞.

What is Schrödinger equation for free particle?

The wave function Ψ(x, t) = Aei(kx−ωt) represents a valid solution to the Schrödinger equation. The wave function is referred to as the free wave function as it represents a particle experiencing zero net force (constant V ).

What is the energy of a free particle?

A free particle is not subjected to any forces, its potential energy is constant. Set U(r,t) = 0, since the origin of the potential energy may be chosen arbitrarily.

What is propagator in quantum mechanics?

Propagator. In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one place to another in a given time, or to travel with a certain energy and momentum. In Feynman diagrams, which serve to calculate the rate of collisions in quantum field theory,…

What is the propagator at spacelike separation used for?

Regarding virtual particles, the propagator at spacelike separation can be thought of as a means of calculating the amplitude for creating a virtual particle- antiparticle pair that eventually disappears into the vacuum, or for detecting a virtual pair emerging from the vacuum.

What is a non relativistic propagator?

Non-relativistic propagators. In non-relativistic quantum mechanics, the propagator gives the probability amplitude for a particle to travel from one spatial point at one time to another spatial point at a later time. It is the Green’s function ( fundamental solution) for the Schrödinger equation.

How to find the propagator for a massive vector field?

The propagator for a massive vector field can be derived from the Stueckelberg Lagrangian. The general form with gauge parameter λ reads With this general form one obtains the propagator in unitary gauge for λ = 0, the propagator in Feynman or ‘t Hooft gauge for λ = 1 and in Landau or Lorenz gauge for λ = ∞.