Origin of Wave Function in Quantum Mechanics (Wave function# 1)
The following picture shows a snapshot of waves from the Coral Sea in Queensland, Australia. We can see ripples of water and if we move along the red line, it’s the water height that’s varying with position and generating the wave.
For every wave there is something that varies/oscillates and creates the form of wave, which is the wavefunction for the corresponding wave. Therefore, ‘height of water level from the flat surface is the wavefunction for these tidal waves.
In a flat-water surface, there is no variation in water level, so wavefunction is zero all across and we don’t see any wave.
In the following sine wave, as you move along x axis, the value of y (= sinx) is changing, causing the generation of the wave, therefore value of y is the wavefunction for the sine wave.
Wave Vs Particle
In physics, wave and particle are two completely different phenomena. Particles are localized, while waves spread out over some region of space. Particles have mass, waves have wavelength.
It started with Light
In classical physics (physics prior to the arrival of quantum physics) an object exhibits properties of one of the two mutually exclusive phenomena: wave or particle. So, scientists expected that, light would be either purely particle or purely wave. However, properties of light made scientists confused from time to time. Sometimes, light exhibited properties of waves, sometimes ofparticles. This has been the root of Quantum Mechanics. Quantum behaviors are most readily observed for microscopic systems (for light/electons, inside atoms and molecules). If you heard that Quantum Mechanics is amazing, shocking, interesting, it’s because of this principle: an object can exhibit both wave and particle properties.
Light behaves both as wave and particle. In terms of the particle nature, light is called photon and as awave it’s the electromagnetic wave. An arbitrary snapshot of an electromagnetic wave is helpful is understanding of wave function.
Though the above image presents a three-dimensional representation, it bears only one-dimensional information: it gives the values of electric and magnetic fields only along the points located on the x-axis. For example, at x= 5, the values of electric field is 10. It doesn’t represent that, light is moving along the sinusoidal curved path, light is actually moving along the horizontal black line with arrowhood.
What we have at this point” electric field (magnetic field) value is the corresponding wavefunction of an electromagnetic wave.
From Photon to Electron: introduction to Wave function
Unless you are dealing with Advanced Quantum Mechanics, a wavefunction usually refers to the wavefunction for an electron.
Electron was discovered in 1911 by Sir Joseph John Thomson and initially it was described as particle. Being inspired by the fact that light behaves both as particle and wave, in 1924, a French graduate student De Broglie, in his PhD thesis hypnotized that electrons can also behave as waves. The hypothesis was experimentally verified in the years 1926–27. This led physicists to a conundrum : Every wave must be associated with a wavefunction (Water height for water wave, Electric/magnetic field for light), so if an electron behaves as wave, what is the corresponding wavefunction? What quantity is varying and generating electron wave?
This question created confusions and raised strong debates among the physicists in the late 1920s, especially in the 5th Solvay Conference year 1927, which was marked by a interactive exchange of arguments between Einstein and Niels Bohr.
Because of varying opinions on what electron’s wavefunction physically mean, it has been more customary to call it simply the general term “wave function”, which is represented by the Greek alphabet Ѱ (psi) (the symbol might seem little scary, though it’s just a symbol like letters A, B).
