A simplistic approach to “The Uncertainty Principle”

Abstract

Throughout the world, almost all of the courses in Physics commence with anintroduction to Newton’s Laws! These laws elegantly describe “our” macroscopicworld. These laws beautifully explained movement of planets, justified ellipticalorbits and helped us in understanding this vast universe including our Solar System.These laws seemed flawless initially but further discoveries challenged Newtonianinterpretation. Newton’s laws couldn’t explain the observations in the atomic arenaand in the cosmic arena. Let us see what has transpired in atomic world sinceNewton through Uncertainty Principle deduced by Heisenberg. We must knowfollowing two variables about a system at any point of reference in time in order tostudy time and space evolution of the system: Position, Momentum. Newton statedthat these physical quantities could be nimbly determined in an experiment to agreat precision. However, things changed drastically with the advent of QuantumMechanics. The birth of Quantum Mechanics was marked by the energyquantisation law given by Max Planck. This new law was the explanation for theUltraviolet Catastrophe related to the black body radiation. Later, a lot of scientistsbuilt upon this subject in a collaborative effort. In this article, the main emphasiswould be on Heisenberg approach which is based on Linear Algebra and matrixmechanics. Heisenberg stated that the position and momentum of a quantumparticle can’t be measured simultaneously with full accuracy. He challengedNewton’s fundamentals with mathematical deductions. He named his newdiscovery very aptly as “The Uncertainty Principle”. This article tries to deduce samemathematical results using a different approach