What is quantum mechanics

After graduating from high school, you haven't seen John for twenty years. Tomorrow there is going to be a class reunion. You imagine what John looks like. In twenty years, John's look must have a quantum change. You really don't know how exactly he will look. Instead, you can imagine infinitely many different looks, each with different probabilities. While you haven't seen John for twenty years, you have seen how other people grow old over time. You can assume the mechanism of John's aging is the same as others. However, you cannot describe John's aging process the same way as others for you don't know the details of his aging over time. You don't even know what John look like right now. Instead, you have to make a probability distribution function whose aging process is guided by the same principle as others whom you are familiar with.

In one second, an electron moves around the atom billions of times. No matter how much you want to shorten the observation period, an electron still moves a lot. There is no way you can track its movement closely. Every time you want to check with the electron, it already makes a quantum change. You can only observe the frequency and magnitude of light emitted from the atoms. From which we can deduce the energy of the states and the probability of transition between the states. You assume the movement of tiny electrons follow the same principle of those large particles, which you can observe directly. However, there is no exact equations available for you to copy. Classical physics doesn't deal with transition probabilities of states of particles.  You have to create new methods to describe their movements. Some of the methods are Heisenberg's matrix mechanics, Schrodinger's wave equation and Feynman's path integral.  

What is Schrodinger's cat

There is a rumor that John's cat is dead. But others insist it is still alive. You have no idea whom to believe. The next day, you are going to visit John's home. At that time, you will know if the cat is alive or dead. At present, it is either alive or dead.