Matter waves are not physical waves. They have phase velocity faster than the speed of light which violates the laws of physics. Their group velocity is smaller than the speed of light. A matter wave travels with group velocity equal to ‘v’ which is also the velocity of an electron present in that matter wave.

All matter exhibits wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave. In most cases, however, the wavelength is too small to have a practical impact on day-to-day activities.

From the standpoint of classical physics, diffraction is impossible in the scattering of particles. Quantum mechanics has eliminated the absolute boundary between the wave and the particle.

de Broglie equation states that a matter can act as waves much like light and radiation, which also behave as waves and particles. Therefore, if we look at every moving particle whether it is microscopic or macroscopic it will have a wavelength.

Apply the de Broglie wave equation λ=hmv λ = h m v to solve for the wavelength of the moving electron. This very small wavelength is about 1/20th of the diameter of a hydrogen atom. Looking at the equation, as the speed of the electron decreases, its wavelength increases.

The wavelength (λ) that is associated with an object in relation to its momentum and mass is known as de Broglie wavelength. A particle’s de Broglie wavelength is usually inversely proportional to its force.

Thus, neutron wavelengths range from 2.8 × 10–14 m (0.00028 Å) or smaller for fast neutrons to 1.8 × 10–10 m (1.8 Å) for thermal neutrons to 4.95 × 10–8 m (495 Å, which is the same wavelength as extreme ultraviolet [EUV] light) for ultracold neutrons.

The de Broglie wavelength of a particle is inversely proportional to its momentum.

De Broglie proposed that as light exhibits both wave-like and particle-like properties, matter to exhibit wave-like and particle-like properties. This nature was described as dual behaviour of matter. On the basis of his observations, de Broglie derived a relationship between wavelength and momentum of matter.

Let’s find the de Broglie wavelength of an electron traveling at 1% of the speed of light. 9.10938356*10-31 kg . The speed of this electron is equal to 1 c divided by 100, or 299,792,458 m/s / 100 = 2,997,924.58 m/s .

Classically a particle is at rest (in some frame) when its velocity and momentum vanish. As indicated in the statement of the Question, the uncertainty principle then tells us that this condition can only be achieved if the particle is in an arbitrarily large box. …