Phi Definition and 130 Threads

Prove that if d divides n then phi(d) divides phi(n). Thanks

Homework Statement Compute the S-operator to first order in the coupling constant lambda. Homework Equations The given Lagrangian density is L = : \frac{1}{2} (\partial_{\mu} \phi)^2 - \frac{1}{2}m^2\phi^2 + \frac{1}{2}\frac{\lambda}{4!}\phi^4 : where phi is a scalar field. The...

Phi is pronounced fi in America, not fee! Bill_Smith is Online: Posts: 0 Fi, not Fee! Okay people, here is the logic behind phi. Yes, in Greece you would pronounce the letter phi as fee. If you lived in Mexico you would pronounce the letter x as eck-ees. In America we pronounce the letter...

Hi, just wondering whether the commutation relation [\phi,L_3]=i\hbar holds and similar uncertainty relation such as involving X and Px can be derived ? thanks

The golden ratio is irrational. Do you know any clever proofs for this fact? I put this here, because it's not homework--only more of a discussion.

what exactly is a quotient set? I know it "partitions" a large group of numbers into discrete subsets but I still don't know what exactly it is in practical terms. Like, does it relate somehow to Euler's phi function?

What do you all think of college honor societies? Specifically, Phi Beta Kappa, and Phi Kappa Phi? Are these things that should definitely be accepted? Or is there really no point to them? Thanks!

Here is the question from the book: ------------ Determine all n for which \phi(n) = n -2. ------------ Now it seems that the only time this will work is for n = 4. However, I haven't any idea of how to prove (or justify) this. I have thought about working primes and composites, since we...

A while back, I found an online applet that was located on the front page of the mathematics department website for some American university. The problem is that I can't remember which university it was, and I'm not succeeding in several searches. Basically, the way it worked was, you type...

Is this inequality true ever and when? 1/2 \phi{(p_{n}^{\sharp})} < \pi{(p_{n}^{\sharp})}-n

Ok the question is as follows: Given gcd(a,b)=d, show that Phi(ab)= (d*phi(a)phi(b))/phi(d) I know that if gcd(a,b)=1 then phi(ab)=Phi(a)phi(b) but I am just stuck here. Any help would be greatly appreciated!

The wave function is a probability amplitude. So far so good. This means that it doesn't give us the probability directly and it can be a complex number. Taking the square modulus of it, gives rise to interference. That's very good. But why the square, why not the fourth power or any even...

Is there anything significant about phi, other than 1 + phi = phi^2 ? Is this just fun number trivia, or is phi actually useful to science, etc...?

DJGriffiths, 3rd ed., Prob 1.37: derive the \hat{r}, \hat{\theta}, and \hat{\phi} unit vectors in terms of \hat{x}, \hat{y}, and \hat{z}. I know the formula and how to find them, but derive them?? ...unless this is what is meant? tia, -LD

As a problem I was asked to show that phi, as defined by: \phi_n(t) = \frac{n}{\pi(1+n^2t^2)} Satisfies the property that for any f with the property to continuious at 0, then: \lim_{n\rightarrow\infty} \int_{-\infty}^{\infty} \phi_n(t)f(t)dt = f(0) But if we let f be 1/phi, we see that it...

What are the Feynman rules for phi to the sixth theory? Can anyone please help? Peskin and Schroeder does phi ^ 4th... I can't help thinking the derivation is the same for phi to the sixth, and that the rules are the same. Could that be correct? Thanks so much for your time, Job...

Anyone else fascinated with the Golden Ratio (Phi)? It seems that there is an underlying principle with everything that is in this world that has some sort of aspect related to Phi. From artwork, proportions of the human body, to the growth rate of biological cells. Everything seems to have...

im having trouble determining the angles of phi in spherical coordinates when asked to convert a triple integral into spherical, and find the limits of the phi integral. can anybody point out any hints/tips/tricks how this may be done??Please...i have an exam tomorrow and I am tryn to prepare...

Does anyone know any practical uses for the number Phi? I have just read a book about it and I am wondering what else it can be used for. Such as in Electronics or mechanical engineering. Thanks! =-)

As a first year physics student, the Greek alphabet bewilders me. I'm sure everyone here has made the mistake of confusing a nu for a v, and yesterday I found out that I am incapable of writing zeta. However, the worst offender in my book is the letter phi. In the E&M textbook I am using (by...

Hey.. .i just read in the Da Vinci Code that phi = 1.68 and that everythin in thie universal has the same proportion.. and that its called the DIVINE Proportion... For example, if you divide the length between your head to ur toe by the length between your waist and toe ur going to get the value...

Phi- normal distribution (how to look normal tables!) hello, can anyone please tell me how to look up values for the following from the "normal table" distribution. \phi^-1(0.25) ans. is -0.68 but i can't figure out how the **** it is so! so please someone reply fast 'cause this...

This is by far the most exciting site on pi and phi I have ever seen. You must see this. http://goldennumber.net/five(5).htm Don't forget to see the side links to other pages in the site that describe other interesting facts.

hi, it's me again, i only have 3 tiny questions then i am done asking, i hope! i need to show that if gcd(a,n)=(a-1,n)=1, then 1+a+a^2...+a^\phi^n^-^1\equiv0 mod n show (m,n)=1 then m^\phi^n+n^\phi^m\equiv 1 mod (mn) show if m and k are positive integers then \phi(^k)=m^k-1\phi(m)...

I was wondering if the number phi (1.618) has ever popped up in modern or classical physics. thanks in advance

ok, so I'm a physics ignaramus. and a spelling one too. but recently i was thinking about what is this thing we call music and why, when u go to a jam concert (Grateful Dead, Phish, Etc.)- you reach something like a meditative state, (yes, even without drugs) and i stumbled upon Ohm...

E = -grad Phi - &A /&t I would like your opinion regarding an explanation I gave elsewhere. I hold that the explanation below is straight forward. However it appears as if some were confused by it. In a certain frame of referance, for a particular electromagnetic field, the relation \partial...

I would like your opinion regarding an explanation I gave elsewhere. I hold that the explanation below is straight forward. However it appears as if some were confused by it. In a certain frame of referance, for a particular electromagnetic field, the relation \partial A/ \partial t = 0 holds...

do those constants have any relation to each other? does something like pi-e or pi/e has any significance?

-hey everyone, this one might be a little too math based for this forum, but I ran across it studying for one of my quantum exams and it seemed like an interesting problem. Haven't figured it out completely. We all know hermitian operators play a central role in quantum and so being able...