Recent content by ibysaiyan

I was under the impression that maybe there is a way of showing the above relation, but now it all makes sense. Thanks for the clarification.

Guys thanks for the responses. My issue is still not resolved. Let me rephrase the question. I want to know how one can show that \int dx/y = \int d(x+y) / (x+y)

This is why I am stumped. I am referring to the bottom most solution posted on the following link by juantheron (user): http://math.stackexchange.com/questions/610733/how-to-integrate-int-dx-over-sqrt1-x2?lq=1

You have misunderstood my post. I want to know why dx/y = dy/x = \int d (x+y) / (x+y) = ln (x+y) + C Thanks.

Homework Statement Hi I am trying to solve an indefinite integral of the form 1/ sqrt[ (x^2 +1)] dx.. Homework Equations The Attempt at a Solution Different ways of solving it are posted on the link below. I would like to know the following result : dx/y = dy/x = d...

Thanks for the explanation, apologies if I have annoyed you.

I was referring to the second part of the question. Suppose f(x) = e^(-1/x) f'(x) = \lim_{h \to 0} e^{(1/x+h)} - e^{(1/x)} / h A taylor expansion about e^-{(1/x)} = \sum_{n=0} ^ \infty - (1/x^n) /n! f'(x) = \lim_{h \to 0} (-1 - 1/{(x+h)}) - (-1 - {1/x}) / h f'(x) =...

This problem has caught my attention.. I was thinking of using binomial expansion for e^(x+h)^-1 term and then to apply e^k -1 / k = 1 as lim k--> 0

Hi vela I have fixed few typos so it should be clear now.

Actually... I think I get it now... (below is what I think happens} Is it because \Phi(x) = -\Phi(-x)(odd) and f(x) = f(-x) (even)... Integral of odd*even = integral of odd = zero . Also for the other two integrals(with exponential) they are defined as "symmetric limited function"...

I was in a rush hence my lack of input. Here is what I get after expansion: \Psi(x,t) = 1/\sqrt{2} (\Psi_{0}(x,t) + \Psi_{1}(x,t) \Psi_{0}(x,t) = \Phi(x) e^{-iwt/2} and \Psi_{1}(x,t) = \Phi_{1}(x) e^{-i3wt/2} \left\langle\psi \left|x\right| \psi \right> = 1/\sqrt{2}...

Hi, Homework Statement A quantum harmonic oscillator is in a superposition of states(below): \Psi(x,t) = 1/\sqrt{2} (\Psi_{0}(x,t) + \Psi_{1}(x,t) \Psi_{0}(x,t) = \Phi(x) * e^{-iwt/2} and \Psi_{1}(x,t) = \Phi_{1}(x) * e^{-i3wt/2} Show that <x> = C cos(wt) ...Homework Equations Negative...

Oh yes, that makes sense. I was getting mixed up between neutron stars and white dwarfs since they both are stabilized by degeneracy pressure. Does this mean the star on the whole is neutral ,as someone else before me suggested (above) but how can it be like that when we know neutron stars have...

Don't neutron stars consist of a sea of degenerate electrons and angular momentum ? Would that have any bearing to their EM spectrum.

Ok.. so I have just used the identified that I previously mentioned.. I still don't end up with the form in the OP. $$\left.\frac{A}{x}\sin k'x\right|_{k-\Delta k}^{k+\Delta k} = \frac{A}{x}[\sin ((k+\Delta k)x) - \sin((k-\Delta k)x)].$$ Now sin (a+b) = sinAcosB+sinBcosA , sin (a-b) =...