Wednesday, 27 June 2018
In this video I want to give you an objective understanding of the waveequation of quantum mechanics. To do this I am going to use an image ofsomething that we all have an objective picture of.
I am going to use the imageof a man pushing a box in the x-direction, now if we want to know where your
box is at a given time we need something called the position function and theposition function is a function that tells you what is the future of X. All you need is to input the time and you will know where your box is at that time. It gives you the future position of the box. The equation that describes the motion of this process is Newton's second law that says that the force is equal to the mass of the box into the second derivative of the position, meaning that if your object is moving there must be a force and this force is equal to the change of speed or the second change in position into the mass. This description of the motion is a differential equation if you solve this differential equation you will get a position function that will give you the future of the system or in other words the future position of the box at given moment in time!
Now if we look at Schrodinger equation we find it is based on the same rules as Newton's second law in the classical system.
The only difference isinstead of representing a box the system is a subatomic particle say a photon electron interaction that behaves like a wave particle. It has a wave particlenature and the equation that describes this behaviour is called the Schrodinger wave equation and solving this equation gives us information on the future of this wave particle duality. Just like our box in classical physics with the future position of the box represented by the position function, in quantum mechanics the future is represented by the quantum wave particle function or probability function.
This great similarity between classical physics andquantum mechanics is not an accident. It is because the ever changing world ofour everyday life that we represent with classical physics is based on the probabilistic nature of quantum mechanics.
In this theory the mathematics ofquantum mechanics represents the physics of ‘time’ as a geometrical process ofenergy exchange with Newton’s differential equation representing processes over a period of time.