Wavefunction Formulate

"The more I think of the physical part of the Schrödinger theory, the more detestable I find it. What Schrödinger writes about visualization makes scarcely any sense, in other words I think it is sh...... The greatest result of his theory is the calculation of matrix elements."

Werner Heisenberg (8 June 1926)

At the mid 1920’s, there was an almost unknown young physicist, an Austrian named Erwin Schrödinger who was trying to develop a general wave mechanics theory to describe observation on the quantum level.

As it turned out now, this wave mechanics was nothing but Heisenberg’s matrix mechanics other side of the coin.( Paul Dirac unified the two mechanics into quantum mechanics.)

Schrödinger developed what is known as Schrödinger equation. This equation states that there is a wave associated with any particle (like the electron), and it is called the wavefunction and it is spread out to fill the whole universe. The wave function is

stronger in one region, which corresponds to the position of the particle and gets weaker farther away from this region but still exists even far away from the “position” of the particle. Schrödinger equation is very good at predicting how particles like electrons behave under different circumstances.

But there is a catch … and a weird… very weird one, and that is when we make a measurement. When we look at an electron, or measure it with a particle detector, the wave function is said to “collapse”. At that instant, the position of the electron is known to within the accuracy allowed by the fundamental laws. But as soon as we stop looking, the wave function spreads out again and interferes with the wave functions of other electrons- and, under the right circumstances with itself. (See the two-slit experiment with electrons)

All of this is precisely quantifiable mathematically and makes it possible to calculate how electrons fly into atoms, how atoms combine to make molecules, and much more besides.

What does all of that mean in plain English?


It means:

There is a fortune teller lady called Schrödinger equation who can predict and describe precisely and deterministically the quantum state of the particle.

However, if you doubt in her ability and decide to check on her by making a “measurement”, somehow she knows that you want to check on her. She gets really mad and wild even before you or her knows the outcome of the “measurement”. At that time

lady Schrödinger equation transforms herself into a “probabilistic fortune teller”, and all what she can tell you are probabilities of various outcomes of your “measurements”.

When you “know” the result of your “measurements”, the weird lady Schrödinger equation gets really crazy and “collapses” or “jumps”. But does she collapse and disappear or jump to a very far place? No, she jumps to the new quantum state which was revealed by your “measurement”, as she is very keen to stay with you so you can ask her again to predict the quantum state until you make the next “measurement”, and so on.

So actually collapse of the wave function is equivalent to saying that we can know where things are, only when we are actually looking at them. Blink and they are gone!

Lady “ Schrödinger equation” tells us too that particles are like shy people. Their behavior depends on whether or not we are looking at them.

Born's Probability Interpretation

Max Born, the famous German physicist took Schrödinger's work a step further. While studying how quantum mechanics describes collisions between particles, he realized that the intensity of the-Schrödinger wave was a measure of the probability of finding the particle at each point in space. In other words, a measurement would always find a whole particle, rather than a fraction of one, but in regions where the wave intensity was low, the particle would rarely be found, whereas in regions of high intensity, the particle would often be found.