Recent content by raopeng

Thanks I got there in the end using that expansion though.

Homework Statement Landau&Lifshitz Vol. Mechanics, p101 Q1Find the moment of inertia of a molecule of collinear atoms Homework Equations The Attempt at a Solution I defined the origin alone the orientation of the molecule. I_3=0 obviously. For I_2 I wrote I_2=Ʃm_b[x_b-\frac{Ʃm_a x_a}{μ}]^2...

Well the mathematical idea is that since for a (n-1) sub-manifold a R^n-1 can be introduced, the orthogonal complement to the hyperplane R^n-1 becomes after a suitable diffeomorphism the normal to the surface in the space, Hence it is possible to write dV=S.h for any n-volume. Then...

In my textbook W=∫p.dV is only proved for a syringe with a piston. This is quite easily done but the book never explains how it extrapolates to the general situation for a gas expanding in any deformable container. It seems the point is to prove dV= S.h where S is the surface area of a given...

det A here means |det A| exp(i \sum_0^n{arg w_i}) where w is the eigenvalue of A. This question even takes 20 minutes to type.. or I really suck at latex..

Homework Statement Verify that \int_{ℝ^n}exp(-\frac{λ}{2} \langle Ax, x \rangle-i \langle x,ζ \rangle )dx=(\frac{2\pi}{λ})^{\frac{1}{2}}(detA)^{-\frac{1}{2}}exp(-\frac{1}{2λ} \langle A^{-1}ζ, ζ \rangle ) where A is a symmetric matrix of complex numbers and <ReA x, x> is positive definite, and λ...

hmm I think trying first to prove the convergence of (x + y)^2 would be a good start..

Eh I suppose here the schedule is not quite the same as in US because EM with all the topics listed above is indeed a first year course, much like in UK I hear. And indeed this causes all kinds of confusion like the homopolar disk and I only got to get a grip at it when learning the more...

I agree with Vanhees71. Some intro calculus would greatly reduce the difficulties of EM. Although here they start the course in the same way from static fields with experiments to electromagnetic effects in which relativity might take a very some portion, some circuits, and Maxwell's Equations...

For example, how far should one go in real analysis or functional analysis to learn the necessary mathematical formalism in Quantum Mechanics? I have some grounding in differential equations, algebra, complex analysis, and rudiments of real analysis included in a classical analysis course. Would...

I feel this pamphlet is a great supplement to any Mathematical Analysis courses, with focus on some introduction to differential geometry and a geometric insight, not a good textbook for self-studies, however, in my opinion due to its conciseness. The book at my hand is a 1960s edition, for a...

My understanding is if we simply rearrange the generalised velocity in the Lagrangian, then generalised momentum is not an independent variable which it becomes under a LT to Hamilton. And then it has a number of advantages for example it is not restricted to different representations of...

I transform the series in this way: Ʃ_{k=1} ^{n} \frac{1}{(1+k/n)^2 n} which turns into an integral \int^1 _0 \frac{dx}{(1+x)^2}. An integration gives 1/2.

Oh thanks so much!

Homework Statement Find the sum using integration: lim_{n→∞} \frac{n}{(n+1)^2} + ... + \frac{n}{(2n)^2} Homework Equations The Attempt at a Solution I think this requires a clever construction of a series of an finite integral which after integration gives the series. Then it can...