I need to use hermiticity and electromagnetic gauge invariance to determine the constraints on the constants. Through hermiticity, i found that the coefficients need to be real. However, I am not sure how gauge invariance would come into the picture to give further contraints. I think the...
I found an explanation for the motivation behind minimising lambda here: (although I am not sure if it answers any doubts) https://math.stackexchange.com/questions/202406/proof-of-cauchy-schwarz-inequality-why-select-s-so-that-so-that-x-sy-wou
I guess this is another way of proving the...
Thanks for the reply.
Can you elaborate on why lambda can't be a maximum?
Also, i think lambda is the independent variable because it can be any complex valued number and minimising the inner product is an important part of the proof.
Yes, it does seem more tedious but I am still confused as to why we treat Px as the origin, i.e. why do we measure the distance from the length element on the x-axis (x-L) from Px as opposed to measuring it from (0,0), where we would
I understand it can be done in a way
which takes advantage of the symmetry of the problem, but i was wondering how to solve it by extending the line charge from 0 to 2L rather than - L to L. I apologize if this seems trivial.
Well when i was working on my soln, i drew a figure where the length of the line charge extendend from 0 to 2L which is different from the book(Griffith drew it from - L to L as you can see from the figure in my post) . So i subdivided the line into two equal x's from the mid point and...
Are you saying that evaluating it over 0 to 2L would not make it symmetric? If that is the case, then if i were to say, shift the line charge L units to the right and put the limits from 0 to 2L would it be correct? I'm abit confused as to why I need to evaluate the integral by specifying the...