If one would apply the principles of special relativity onto QM, YES !Harmony said:
Stationary with respect to what frame ?
The de broglie wavelength is a property of a single particle (corresponding to a single energy eigenstate) while a density function describes a group of particles (ie the corresponding wavefunction is a superposition (or tensor product like a Fock space) of single particle wavefunctions which in themselves can contain multiple energy eigenstates if they are non stationary and thus exhibit a spread in their momentum or "deBroglie wavefunction"). So, no straightforeward relation, IMO.Truth Finder said:
The De Broglie wavelength is a concept in quantum mechanics that describes the wavelength of a particle with mass. It is named after French physicist Louis de Broglie, who proposed that all particles, including matter, have both wave-like and particle-like properties.
The De Broglie wavelength is inversely proportional to the velocity of a particle. This means that as the velocity of a particle increases, its De Broglie wavelength decreases. This relationship is described by the equation λ = h/mv, where λ is the De Broglie wavelength, h is Planck's constant, m is the mass of the particle, and v is its velocity.
The De Broglie wavelength is significant because it demonstrates the wave-particle duality of matter. It shows that even particles with mass, such as electrons, can exhibit wave-like behavior. This concept is fundamental to understanding quantum mechanics and the behavior of particles at the atomic and subatomic level.
Yes, the De Broglie wavelength can be measured using various experimental techniques, such as electron diffraction or neutron scattering. These methods involve passing particles through a diffraction grating or crystal and measuring the resulting interference pattern. The wavelength can then be calculated using the diffraction equation.
The De Broglie wavelength of stationary matter, such as a particle at rest, is equal to its Compton wavelength. This is the minimum wavelength at which a particle can be observed, and it is inversely proportional to its mass. For example, an electron at rest has a De Broglie wavelength of approximately 2.4 × 10^-12 meters, which is also its Compton wavelength.