and Johansson P.I.Developing de Broglie Wave [ ]
The probability amplitude looks like a wave and the Schrödinger equation is a wave equation.
andBorissova L.Exact Theory to a Gravitational Wave Detector.
Two specific examples supporting the wave nature of electrons as suggested in the are the discrete atomic energy levels and the diffraction of electrons from crystal planes in solid materials. In the Bohr model of atomic energy levels, the can be visualized as "wrapping around" the circumference of an electron orbit in such a way as to experience constructive interference.
In 1924, argued that if photons, with their known wavelike properties, could be described as particles, electrons as particles might show wavelike properties with a wavelength λ inversely proportional to their momentum p = m_{e}v.
De Broglie–Bohm theory  Wikipedia
We believe that teaching and understanding quantum mechanics would be much simpler if we called the " function." It only looks like a wave in simple cases of configuration space.
In a quantum world describable by the unitary evolution of the deterministic Schrödinger equation, nothing new ever happens, there is no new "outcome." Outcomes are added to standard quantum mechanics by the addition of the "projection postulate" or "collapse of the wave function" when the quantum system interacts with another system.
What is the significance of de Broglie's equation?  …
If you explore the wavelength values for ordinary macroscopic objects like baseballs, you will find that their DeBroglie wavelengths are ridiculously small. Comparison of the power of ten for the wavelength will show what the wavelengths of ordinary objects are much smaller than a nucleus. The implication is that for ordinary objects, you will never see any evidence of their wave nature, and they can be considered to be particles for all practical purposes.
We believe that teaching and understanding quantum mechanics would be much simpler if we called the " function." It only looks like a wave in simple cases of lowdimensional coordinate space.
put forward an idea which is known as de Broglie Hypothesis ..

Is de Broglie matter wave a mass or a particle hypothesis?
C.An Explanation of De Broglie Matter Waves in Terms of the ElectronCoupling to the Vacuum State [ ]

I'm having difficulty understanding de Broglie matter wave hypothesis
C.The de Broglie Relations Derived from the Electron and Proton Couplingto the Planck Vacuum State [ ]

de Broglie Equation Matter and its wave nature  Physics
C.The Compton Radius, the de Broglie Radius, the Planck Constant, and theBohr Orbits [ ]
Quantum Mechanics De Broglie matter waves ..
Although Einstein sometimes referred to it as a "ghost field," and later developed a "pilot wave" theory in which waves guide the motion of material particles along paths perpendicular to the wave fronts, the wave function ψ has no ponderable substance.
DeBroglie Hypothesis  Engineering Physics Class
Animation of a probability amplitude wave function ψ collapsing  Whereas the abstract probability amplitude moves continuously and deterministically throughout space, the concrete particle, for all we know, may move discontinuously and indeterministically to a particular point in space.
Wave Nature of Matter and De Broglie’s Equation
As put it, the equations of motion for the probability waves are deterministic and continuous, but the motion of a particle itself is indeterministic, discontinuous, and probabilistic.
Debroglie hypothesis  Brilliant Math & Science Wiki
Planck applied Boltzmann's statistics of many particles to radiation and derived the distribution of radiation at different frequencies (or wavelengths) just as and Boltzmann had derived the distribution of velocities (or energies) of the gas particles.
broglie hypothesis  Matter wave  Wikipedia
There is no logical contradiction in the use of the deterministic Schrödinger wave equation to predict values of the (indeterministic) probability amplitude wave functions at future times.
DeBrogle's Hypothess and Matter Wave  …
Schrödinger attempted to interpret his "wave function" for the electron as a probability density for electrical charge, but charge density would be positive everywhere and unable to interfere with itself.