Based on an intuitive feeling that nature is symmetrical, Louis deBroglie (de-broy-lee) made an argument in 1924 that if waves have a particle nature, then particles must have a wave nature.
He began with the formula for momentum of a photon, solved it for wavelength, then replaced momentum with mv (particle momentum).
For any particle with even a small amount of mass, the wavelength is very small. Even the electron has a very small wavelength. Protons or Neutrons have even smaller wavelengths since they have more mass. Theoretically, any moving matter has wave characteristics. However, the wavelength of any life-size particle, like a golf ball, is so small that it is immeasurable.
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