Wave-Particle Duality

One of the major phenomenon that can't be explained by classical mechanics is the wave-particle duality.

Light waves act like particles and particles act like waves.

          Fig: Wave-Particle duality

Particle nature of light explains photoelectric effect and black body radiation. Wave nature of light explains the phenomenon of interference and diffraction. 

Wave-particle duality is the ability of a matter to behave as a wave or particle. 

The Schrodinger equation determines the allowed wave functions for the system and how they evolve over time. A wave function behaves qualitatively like other waves such as water waves and waves on a string, because the Schrodinger equation is mathematically a type of wave equation. This explains the name 'wave function' and gives rise to the wave -particle duality. 

The wave of the wave function is not a wave in physical state, it is a wave in an abstract mathematical "space" and in this respect it differs fundamentally from water waves and waves on a string. 

Here's one of the quirky things about quantum mechanics ; just because an electron or a photon can be thought of as a particle, doesn't mean they can't still be thought as a wave as well. In fact, in lot of experiments , light acts much like a wave than like a particle. 

Scientists interpret quantum mechanics to mean that a tiny piece of material like a photon or electron is both a particle or a wave. It can be either, depending on how one looks at it or what kind of an experiment one is doing. In fact, it might be more accurate to say the photons and electrons are neither a particle nor a wave. 

There is a theory by Werner Heisenberg called the uncertainty principle. It states that if a researchers wants to measure the speed or position of a particle, he can't do both very accurately. If he measures the speed carefully, then he can't measure the position nearly as well. 

Summary :

The only way to resolve this problem is to accept the idea that light possesses both particle and wave like properties. Thus light has dual nature, i.e, it behaves as a wave and as a stream of particles.