Fundamental Equations of Quantum and Classical Mechanics  
 
 
In classical mechanics, or the physics of our everyday world, the fundamental equation of motion is referred to as Newton's Second Law or Force equals Mass times Acceleration.
The mass 'm' is familiar to us all as the quality which determines the property of 'heaviness'. We know that more massive objects are heavier objects. Force is the property required to lift these objects and acceleration is what we feel when our vehicle changes from being still to being in motion. Acceleration is represented here as the second time derivative of displacement 'x' rather than the parameter 'a'.
From this simple equation which relates quantities from our everyday experience, we can derive mathematical models which successfully predict the motion and position of objects and structures in various and complex situations within our world.
As discussed earlier this equation and these models, are much less successful when we apply them to objects on the scale of atoms and electrons. For this reason quantum theory was developed around another fundamental equation. This one is known as the Schrodinger Equation.
This relationship shows us how to calculate the wave function which we can interpret as the probability distribution describing our chance of finding the particle in question at any particular location (r,t) in space and time respectively. Other parameters are defined as follows.
This equation lacks the intuitive foundation we find in Newton's Second Law but it has come to be accepted for the very same reason as Newtons's Laws, and that is that 'it works!'
The history of how this equation came into being is fascinating and instructive, however the interested reader is invited to procede guilt free from this point forward if they choose to just believe the equation and carry on to learn more about how it can be applied to give results which provide utility in our daily lives.
