A simplistic approach to “The Uncertainty Principle”

Throughout the world, almost all of the courses in Physics commence with an introduction to Newton's Laws! These laws elegantly describe “our” macroscopic world. These laws beautifully explained movement of planets, justified elliptical orbits and helped us in understanding this vast universe including our Solar System. These laws seemed flawless initially but further discoveries challenged Newtonian interpretation. Newton's laws couldn't explain the observations in the atomic arena and in the cosmic arena. Let us see what has transpired in atomic world since Newton through Uncertainty Principle deduced by Heisenberg. We must know following two variables about a system at any point of reference in time in order to study time and space evolution of the system: Position, Momentum. Newton stated that these physical quantities could be nimbly determined in an experiment to a great precision. However, things changed drastically with the advent of Quantum Mechanics. The birth of Quantum Mechanics was marked by the energy quantisation law given by Max Planck. This new law was the explanation for the Ultraviolet Catastrophe related to the black body radiation. Later, a lot of scientists built upon this subject in a collaborative effort. In this article, the main emphasis would be on Heisenberg approach which is based on Linear Algebra and matrix mechanics. Heisenberg stated that the position and momentum of a quantum particle can't be measured simultaneously with full accuracy. He challenged Newton's fundamentals with mathematical deductions. He named his new discovery very aptly as “The Uncertainty Principle”. This article tries to deduce same mathematical results using a different approach.