In the framework of quantum mechanics, the concept of wave-particle duality suggests that all particles, including fundamental particles such as electrons, protons, and photons, exhibit both wave-like and particle-like behavior. The wave-like behavior is described by a mathematical entity called the wave function.
The mathematical formalism of quantum mechanics, which includes the Schrödinger equation for non-relativistic particles or the more general framework of quantum field theory for relativistic particles, treats particles as wave-like entities. These mathematical equations describe the evolution of the wave function of a particle, which can be interpreted as a probability amplitude for various outcomes when measurements are made.
While there may not be a single specific theoretical paper or argument that conclusively proves the existence of a wave associated with every kind of particle in nature, the wave-like behavior of particles is a fundamental aspect of quantum mechanics and is well-established through extensive experimental confirmation.
The success of quantum mechanics in explaining a wide range of phenomena, including the behavior of subatomic particles, the structure of atoms, and the interactions of particles in particle accelerators, provides strong evidence for the wave-particle duality. Additionally, the predictions of quantum mechanics have been tested and verified in numerous experiments, which support the wave-like nature of particles.
It's worth noting that the wave-like behavior becomes more prominent for particles with small masses or high energies, as described by the de Broglie wavelength. For macroscopic objects, the wave-like behavior is negligible due to the very small de Broglie wavelength associated with their large mass and low velocities.
In summary, while there may not be a single specific theoretical paper that directly proves the existence of a wave associated with every particle, the wave-like behavior of particles is a well-established and fundamental aspect of quantum mechanics, supported by extensive experimental evidence and the success of the theory in describing the behavior of particles in the microscopic world.