Does the de Broglie model assert that an electron must be moving in order to have wave properties?
Yes. It must have velocity and momentum. Otherwise you cannot assign a wavelength to it.
But of course. There exists absolute rest and it can be verified -- or absolute velocity measured as wavelength -- in the dual slit experiment.
The de Broglie model, also known as the de Broglie hypothesis, states that all particles, including electrons, have wave-like properties. According to this hypothesis, every particle with a momentum (including stationary particles) exhibits wave characteristics. Therefore, an electron does not necessarily have to be moving to have wave properties.
To understand why the de Broglie model asserts this, we need to delve into the principle of wave-particle duality. In quantum mechanics, particles exhibit both wave-like and particle-like behaviors. This means that particles, such as electrons, can have characteristics typically associated with waves, such as diffraction and interference. These wave-like properties are described by the wavelength associated with the particle's momentum.
According to the de Broglie hypothesis, the wavelength of a particle is inversely proportional to its momentum. The equation that relates the wavelength (λ) to the momentum (p) is λ = h/p, where h is Planck's constant. This equation implies that even a stationary particle, like an electron at rest, still possesses a non-zero wavelength. Therefore, the de Broglie model suggests that electron wave properties are not dependent on the particle's motion.
In summary, the de Broglie model states that all particles, including electrons, exhibit wave-like properties regardless of their motion. This is because wave-particle duality suggests that certain quantum particles have characteristics associated with both waves and particles.