Yes, light can indeed be described as both particles and waves. This duality is known as wave-particle duality and is a fundamental concept in quantum mechanics.
According to classical physics, light was understood as a wave phenomenon. This wave nature of light can be described using mathematical equations, specifically the wave equation. These equations govern the behavior of light waves, such as interference and diffraction.
However, in the early 20th century, experimental observations led to the development of quantum mechanics, which introduced the concept of particles called photons. Photons are discrete packets of energy that carry the properties of both particles and waves. They exhibit wave-like properties, such as interference and diffraction, as well as particle-like properties, such as the ability to interact with matter as discrete entities.
Mathematically, the behavior of light can be described using different formalisms depending on whether you want to emphasize the wave-like or particle-like nature. For the wave-like behavior, you can use equations like the wave equation, which describes the propagation of light as a wave through space. This equation is a partial differential equation that relates the spatial and temporal variations of the electric and magnetic fields.
On the other hand, for the particle-like behavior, the mathematical framework of quantum mechanics is used. In quantum mechanics, light is described by a wave function, which is a mathematical function that evolves over time and encodes the probabilities of different outcomes when measuring properties of light. The wave function obeys the Schrödinger equation, which governs the evolution of quantum systems.
The duality of light as both particles and waves can be further understood through experiments like the double-slit experiment, where light exhibits interference patterns suggesting its wave nature, but can also be detected as individual particles hitting a screen, indicating its particle nature.
In summary, light can be described as both particles (photons) and waves, and the mathematical descriptions depend on the specific aspects of light's behavior being emphasized, with classical wave equations for wave-like behavior and quantum mechanics for particle-like behavior.