Recent content by DiogenesTorch

Homework Statement Show that for a two spin 1/2 particle system, the expectation value is \langle S_{z1} S_{n2} \rangle = -\frac{\hbar^2}{4}\cos \theta when the system is prepared to be in the singlet state...

In Grifftiths Intro to Quantum 2nd edition, page 51, he is re-expressing the Schrödinger equation for a harmonic oscillator in terms of a unit-less quantity \xi \equiv \sqrt{\frac{m\omega}{\hbar}}x So Griffiths takes the Schrödinger equation in equation [2.70] -\frac{\hbar^2}{2m}...

Cool just wondered if it ever mattered. Thanks Shyan much appreciated :)

lol the extra special sauce. Seriously though I just wondered if somewhere the use of the negative sign has some sort of a practical reason. Like for example when solving partial differential equations using the separation of variables method, we sometimes for convenience stick a minus sign in...

I have noticed the following 2 different forms for the Sturm-Liouville equation online, in different texts, and in lectures. [p(x) y']'+q(x)y+\lambda r(x) y = 0 -[p(x) y']'+q(x)y+\lambda r(x) y = 0 Does it make a difference? I am guessing not as the negative can just be absorbed into...

Thanks Pranav. Looking back this has to be only for definite integrals as ##x## was a change of variable for a frequency relationship, ##x=\frac{\hbar\omega}{k_b T}##. So it has to be only for definite integrals over ##0<x<\infty##.

Thanks micromass, So is the series solution above okay are am I totally off on it?

Is this acceptable? Can we do this? If x is taken to always be positive then: \begin{align*} \frac{1}{(e^x-1)} &= \frac{e^{-x}}{1-e^{-x}} \\ &= e^{-x}\frac{1}{1-e^{-x}} \\ &=e^{-x}\sum_{n=0}^{\infty}e^{-nx} \\ &=\sum_{n=0}^{\infty}e^{-(n+1)x} \\ &=\sum_{n=1}^{\infty}e^{-nx}...

Homework Statement This is the integral \int \frac{x^2}{e^x-1}dx Homework Equations Can this even be solved in closed form? The Attempt at a Solution Only method I can think of is integration by parts over numerous steps. I did that until I get the following: \int...

Homework Statement How to derive equation (22) on page 31 of Kittel's Intro to Solid State Physics 8th edition. The equation is: 2\vec{k}\cdot\vec{G}+G^2=0 Homework Equations The diffraction condition is given by \Delta\vec{k}=\vec{G} which from what I can surmise is the starting...

Homework Statement "A metal bar which runs on 2 long parallel rails are connected to a charged capacitor with capacitance C and a resistor with resistance R. Assume no friction and perfect conductors. The rails are cylindrical of radius R separated by distance d. The bar is a distance x...