“ Anyone who thinks they can talk about Quantum Mechanics without getting dizzy hasn’t yet understood the first word of it. “ - Niels Bohr Quantum Mechanics is not something that can be predicted by using normal senses or intuition. From the dawn of civilization,we’ve been doing basic physics.Even in the stone ages,when someone threw a brick at us,we didn’t calculate the trajectory or the velocity vector of that brick to know where it’s path. We used our intuition,in a macroscopic world, we learned to predict as we became more and more evolved species.Everything follows our intuition when we do something in our day to day life,by using our classical mechanics and logical absolute way of thinking. But things are different in a microscopic level,those things are beyond our senses,and classical mechanics fails to describe it in an orderly manner. I think our leap into microscopic world started when we really tried to push classical mechanics to objects at a very small level,in...
What is a linear Diophantine Equation? The simplest linear Diophantine equation takes the form ax + by = d , where a , b and c are given integers. The solutions are described by the following theorem: This Diophantine equation has a solution (where x and y are integers) if and only if c is a multiple of the greatest common divisor of a and b . Moreover, if ( x , y ) is a solution, then the other solutions have the form ( x + kv , y − ku ) , where k is an arbitrary integer, and u and v are the quotients of a and b (respectively) by the greatest common divisor of a and b . (source: wiki) To know whether a linear diophantine equation has integer solutions, we...