by Anthony Salib | Nov 28, 2017 | Pure Maths

We have alas reached the final leg of our journey, we will continue with the idea of a normed vector space and then we will describe Banach spaces and Hilbert spaces. Associated with the norm on our vector space , is the metric So is endowed with a...
by Anthony Salib | Oct 2, 2017 | Pure Maths

As promised, we begin our quest today in understanding what a normed vector space is. We will begin with a vector space , and we would like to give it some structure similar to our metric spaces. Now we could of course give any metric to , but we already have two...
by Anthony Salib | Sep 30, 2017 | Pure Maths

We left the last post on a cliff hanger, namely that in any given metric space, Cauchy sequences need not converge. Now if you’re reading this, you have chosen to take the red pill, and I’m here to show you just how the deep the rabbit hole goes. We shall...
by Anthony Salib | Sep 27, 2017 | Pure Maths

So in the last post I talked about wave functions being vectors that live in Hilbert space. In this post, I would like to describe the mathematics of Hilbert space, but before we do that we have to go on a journey, a journey through space(s)! The first type of space...
by Anthony Salib | Aug 15, 2017 | Physics

In quantum mechanics, we cannot speak of the exact location of a particle, but rather, we talk about the probability of a particle being in a certain region of space. Mathematically, we describe this using a probability density function, known as the wave function,...
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