Have you ever seen a more beautiful equation??!! Its the kind of thing you would want to put on a T-shirt!
Solving the Schrodinger equation provides scientists with a mathematical quantity called the wavefunction. This wavefunction is a probabilistic determination of where a particle might be at any one time. For example in the case of the electron, the wavefunction DOES NOT tell us the precise location of where the electron is at any moment in time , but rather it represents a “cloud” of probability of where we might find the electron, -if we were to look for it.
At any point in space the wavefunction is assigned two numbers. The probability of the electron being within this tiny volume is the sum of the squares of these two numbers.
I still find that amazing. But that’s not even the beginning of how weird Quantum Mechanics REALLY IS:
-Particles can and do behave both as particles and as waves.
-Particles can be at more than one place at any one time, irrespective of how far away the two places are.
-Particles that have at one time come in contact with each other and are then separated, instantaneously ALWAYS KNOW what the other particle is doing, again, irrespective of how far apart they have moved from one another. Einstein called this “spooky action at a distance”.
Quantum Mechanics is magical, beautiful, unpredictable, strange and unconventional beyond anything ever imagined. Quantum Mechanics defines a lower level of unpredictability that permeates all of our lives. That is why notions of destiny and pre-ordained lives as well as all notions of “it was written, it had to be” go out the window. NOTHING is written. We make our own destiny, in as much as we influence it, others more, others less.
(equation re-printed from the book Quantum: A Guide for the Perplexed by Jim Al-Khalili)