A Simplified Explanation to Wave Function (Wave function# 2)
We saw in part# 1 that, the light wave was generated by the varying electric and magnetic fields. Scientists were in a puzzle, what would be the varying quantity that generate electron wave. What would that mean physically?
A group of scientists came up with an weird idea to describe electron wavefunction: wave of probability. As an arbitrary example, the following wave is generated by a varying value of probability.
A varying probability can generate a wave
In the left, the probability of finding an electron is different at different locations along the x-axis. These different values of “probability for finding an electron” generate a wavelike pattern. If you run an experiment to find the location of an electron, for a particular experiment: it can be found at any value of x, but more likely to be found at x with the yellow marked point.
How Wave Function comes into play
We saw that probability can create a wave pattern, but what is the role of wave function? Loosely, wave function is something, a squre of which gives you the probability. Therefore, you can make an estimate of the probability once you know the wavefunction.
There is a wave function associated with each electron, the expression of which depends on the system (number protons, other electrons etc). If you would like to estimate where the electron is likely to be found, take the square of the wavefunction. (rigorously, you have to take the square of the absolute value of wave function because wave functions can be complex quantities, skip the sentence if getting complicated)
The wave function of light wave is Electric field value, which is a physical quantity, in fact, all kinds of wave functions known to the physicists till the advent of electron’s wave, were physical quantities (that could be measured, experienced). In this situation, the idea of wave of probability, which was not physically intuitive, was less welcoming and left many physicists confounded, if they should accept it!
Why do we need to rely on Probability (wave function)?
If you want to determine the location of an electron in an atom, you will find different locations at different times even though the external conditions are exactly same each time. This is NOT because electrons are rotating around the nucleus and you simply find at different positions in it’s orbit. This is because, electron is a wave before you locate it and once you locate it’s position, now it’s a particle. That the weirdness, the same entity behaves as wave or particle depending upon you observe it or not.
Although we can speak of the wave function that describes an electron as being spread out in space, this does not mean that the particle itself is thus spread out. When an experiment is performed to detect electrons, for instance, a whole electron is either found at a certain time and place or it is not; there is no such thing as a 20 percent of an electron. However, it is entirely possible for there to be a 20 percent chance that the electron be found at that time and place.
