In quantum theory, entities such as particles are described by mathematical objects called wave functions. Wave functions represent the state of a quantum system and contain information about the probabilities of various outcomes when measurements are made on the system.
While it is true that particles in quantum theory do not strictly conform to our classical notion of a wave or a particle, the term "wave-particle duality" is often used to describe their behavior. This duality refers to the fact that particles in quantum mechanics can exhibit properties of both waves and particles, depending on how they are observed or measured.
However, it is important to note that the wave-particle duality is not a complete or comprehensive description of the nature of quantum entities. The behavior and properties of quantum systems are more accurately captured by the formalism of quantum mechanics, which goes beyond the classical concepts of waves and particles.
In quantum mechanics, particles and other quantum entities are described by wave functions, and the evolution of these wave functions is governed by mathematical equations such as the Schrödinger equation or the Dirac equation. The wave function provides a mathematical representation of the quantum state of a system, encompassing its possible outcomes and their associated probabilities.
So, to answer your question, in quantum theory, the entities we study are described by wave functions and the formalism of quantum mechanics, which goes beyond the classical notions of waves or particles. They are fundamentally quantum entities, described by mathematical objects that capture their probabilistic behavior and wave-like aspects.