A voyage through space(s) (Part IV)

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...

A voyage through space(s) (Part III)

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...

A voyage through space(s) (Part II)

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...

A voyage through space(s) (Part I)

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...

Collapse that wave function!

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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