The concept of wave-particle duality in quantum mechanics does not require the presence of a physical medium for the wave-like behavior. Unlike classical waves that propagate through a material medium, such as sound waves in air or water waves in liquid, the wave-like behavior of particles in quantum mechanics is described by mathematical wave functions that do not require a physical medium.
In quantum mechanics, particles, such as electrons and photons, are not thought to be composed of any material substance that is waving through a medium. Instead, the wave-like behavior is attributed to the mathematical nature of the wave function associated with the particle. The wave function represents the probability distribution of finding the particle at different positions in space.
The wave-like behavior of particles is not a mechanical waving of a physical substance but rather a mathematical description of the probability amplitudes associated with the particle's potential positions. These probability amplitudes can exhibit interference and diffraction phenomena, similar to classical wave behavior, even though there is no medium physically waving.
It's important to note that the wave-particle duality in quantum mechanics is a unique aspect of the theory and does not require a classical wave model with a medium. The wave function and its associated probabilities capture the probabilistic behavior of particles, allowing for wave-like interference and particle-like interactions without the need for a material medium.