Dear All,
thanks for your replies. Yes, I have learned EM theory and understand that one can uses Mathematica for generating the data. But that would be really tedious. I shall try to use the free softwares suggested by gsal. In fact, the detector will have extremely small Bz...
Dear All,
I need to design a magnetized iron calorimeter detector (HEP ex). There will be current coils (in the vertical plane) that will generate x-y magnetic field within iron. Given the detector boundaries and exact locations of the coils (i.e. all the B.C.s), I need to obtain the...
Well, of course you are right...But, what I was expecting is a bit different...I was wondering if this integral could somehow be related to Gaussian curvature. The physics motivation is that for some specific type of surfaces, the integral which apparently may also be written as...
Hello everyone,
I am self teaching some elementary notions of differential geometry. Rather, I should say I am concentrating on mean and gaussian curvature concepts related to a physics application I am interested in. I see one has to evaluate an integral that goes as...
I agree fully...The scope of canonical transformations is a larger than the so-called symmetry transformations...Thank you very much for the explanations...
Thanks for the reply...I think I see your point; in such a case, apparently p\rightarrow P is a linear map...By the way, if it was intended, I could not understand the appearance of '!' and '-' sign.
The following question seems to be simple enough...Anyway, I hope if someone could confirm what I am thinking.
Is canonical transformation in mechanics unique? We know that given \ (q, p)\rightarrow\ (Q, P), \ [q,p] = [Q,P] = constant and Hamilton's equations of motion stay the same in the...
In fact, it looks like a Lie group with r being the continuous parameter. With continuous variation of r, apparently all the group elements can be generated starting from the identity...
I am trying to give an answer to the question; please rectify me if I am wrong...Consider points on the radius of a sphere of radius a. The inverse transformation is given as \hat{I}(r)=\frac{a^2}{r}...We are trying to see if the set of all inversions form a group.
Identity...
I am sorry I could not formulate the question properly; it was a mistake to enquire about the group property of all the points lying on a radius of a sphere. Since, I am interested in finding the inversion (in a sphere) operator, the question I should have asked is if the set of all inversions...
Well, the points P_n are such that OP_n\subset(0,\infty) where O is the center...Then, my set members are all these numbers OP_ns. One can multiply them to get another number in this set...Identity and inverse exist. Associativity also works...so they form a group...
However, now I do not...
I think there is some communication gap here...I was not talking about the points on the sphere forming a group under multiplication...this is what I had written:
however, let me think more, for I don't think I can take simple arithmetic multiplication of the distances as the group law...
@Vargo: I am talking about the transformation you have written down. However, this is not all. I want to see the operator \hat{I} that induces such a transformation.
@muphrid: I followed your calculation...Jacobian indeed proves to be a very powerful tool...
I found the Jacobian of this...
I guess you are right...I was thinking in terms of QM where we deal with linear operators...
In QM, a transformation in the real ℝ^3 induces an unitary transformation in the Hilbert space. Let's say, we have a given wave function \psi(x) in a given reference frame(un-primed coordinates). We...