Waves are ubiquitous. Light – the ultimate stuff that powers our whole planet - is a form of electromagnetic waves. Radio – the process with which we have built today’s connected world – also takes the form of electromagnetic waves. Sound – the stuff that enables us to hear, is another example of waves. Particles – the stuff that makes up everything - exhibit fundamental wave property. If this does not sound everything to you, then gravity, which can reveal itself after travelling through the space and time for billions of years through the propagation of gravitational wave giving us a brand new approach of observing our universe, gives us another example.

What is more impressive is the equations that govern light and sound, which are completely different physical identities, are essentially identical to each other. The equation reads $$\frac{\partial^2 \phi}{\partial t^2} - c^2 \nabla^2 \phi = 0,$$ where $\phi$ is the physical variable describing the waves, such as the pressure for sound waves, and $c$ is the speed at which the wave travels. Although linear, the above equation can become very difficult to solve when complicated sources and/or boundary conditions are given.

On the other hand, the equation that describes quantum phonomenon is different, it takes the form of Schrodinger equation when relativity is not considered, i.e. $$i \hbar \frac{\partial \psi}{\partial t} + \frac{\hbar^2}{2m} \nabla^2 \psi - V\psi = 0,$$ where $\psi$ is the amplitude of the probability wave, $\hbar$ is the reduced Planck constant, $m$ is the particle mass and $V$ is the potential energy of the particle described. Although different from conventional wave equations, many techniques used to solve Schrodinger equation are virtually identically to those for sound and electromagnetic waves.