Recent content by zeronem

I’ll admit that statement about Q does not convey the information I am trying to come across with. Basically trying to state that Q is a nonempty subset of R that is a bounded interval (r,s). I wrote it rather quickly without thinking much on it. I admit it needs revision. Basically I’m...

A least upper bound can be considered an upper bound correct? Or in the set of upper bounds. So if I show that x is an upper bound, then of course I have to show it is a least upper bound which seems easier than said. If I show x is an upper bound in A then does that show that x is a least...

I actually had a proof started out like that and ascertained that x is an upper bound. So do I employ density of rationals to show that x is a least upperbound given there exists an element greater than x that belongs to set B? But is not in A. I was able to show inf B = x, where $$ B = \{s...

I ascertained two separate nonempty sets A and B and I was able to prove inf B = x but having trouble with sup A. Where $$ (r,x) \subset A $$ and $$ (x,s) \subset B $$ I also decided to employ Archimedian principle and density of rationals to both sets separately to try to arrive to the...

10-4 thanks for the suggestions. I’m self learning and I appreciate anyone who would be equivalently critical as if they were grading the answer in school. Edit message: Now if I employed the definitions of LUB and GLB in the middle of the proof to give the professor the understanding of...

Ok I put it in the edit

Yea hold on. Took me forever to type this out haha. Let me show you where Archimedean principle and density of rationals come into employment. I’ll do it though edit

I’m using the Archimedean principle with and the density of rationals for my proof. Not sure where you are getting “q”

$$r<x<s$$ $$s-r>0$$ We enploy the Archimedean principle where $$n(s-r)>1$$ We employ density of rationals where $$\exists [m,m+1] \in Q$$ Such that $$nr\in [m,m+1)$$ Therefore $$m\leq nr \lt m+1$$$$ \frac m n \leq r \lt \frac m n + \frac 1 n $$ Since $$ \frac m n \leq r $$ Then $$...

The book describes that the beam splitter is a half coated piece of glass as I’ve stated before. And I think I really meant a ratio between reflection and transmission. My bad wording it angle of reflection, not the right choice of words but when I think about a piece of coated glass being...

Thanks that’s what I figured. So in the exercise problem I must derive my own Ubs for a ratio of 70/30 and that is what I expected. I just wanted to make sure I was going the right route before I get any further with the derivation since the book doesn’t exactly throw in the universal formula...

I guess what I’m struggling with is whether the probability of a photon is dependent on the percent of reflection of a beam splitter, which is just a piece of glass with a semi-reflecting coating as stated in the book. I’m only focusing on the first beam splitter of the interferometer. In...

Ah, Ok. I understand. I’m working off a book authored by Pieter kok titled “A first introduction to Quantum Physics.” So the probability of a photon is dependent on the ratio setup of the beam splitter? The diagram is the type of interferometer setup I’m dealing with, a beam splitter and...

I know that my question is probably simple but I’m wording it too complicated. My question is this, for two detectors in an interferometer there is a probability of exactly 1/2 per detector. So if there were a three detector setup on an interferometer would the photon probability be 1/3 per...

I believe the bean splitters they use in the book is the simple glass plate with coating inside. I’m working out an exercise problem in the book that explains that beam splitter this time around has a 70/30 ratio in reflection. Given that they formed a Ubs operator in chapter off a beam...