Reciprocal Definition and 166 Threads

How do I start to evaluate this integral? \int\frac{1}{\ln x}-\frac{1}{(\ln x)^2} dx I tried subbing u=\ln x but I'm getting no where... The answer is [tex]\frac{x}{\ln x}+C[/itex] If I differentiate the answer, I get the integral easily, but the reverse... I'm having trouble figuring out...

In real space in crystal, strain-induced change can be written as follows: {\bf r'}=(1+\epsilon)\cdot {\bf r} But there is no way to evaluate the strain-induced change in reciprocal space. Can one calculate the strain-induced change in high-symmetry point in quasi-momentum space? I check almost...

Is anybody aware of how to solve the following infinite sum: \sum\frac{1}{n^2} for all positive odd integers? Is this the sort of thing you just look up in a math table or solve? If math table, do I need a "sum of reciprocal powers" table or a "riemann zeta function" table? If...

I came across this question where there is a FCC lattice. It states that the lattice is a convolution of the simple cubic (whose reciprocal lattice is itself) with a basis (that consists of 2 points). When finding the reciprocal of this BCC lattice, FourierTransform(BCC) =...

I understand how this works: \cos x = \frac{1}{0!} - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \frac{x^8}{8!} - \frac{x^{10}}{10!} + \ldots But what about this? \frac{1}{\cos x} = \frac{1}{0!} + \frac{x^2}{2!} + \frac{5x^4}{4!} + \frac{61x^6}{6!} + \frac{1385x^8}{8!} +...

given any two numbers a,b and an upper and lower bound for the sum of reciprocals of a certain class of integers between a and b, without any direct calculation how can optimal upper and lower bounds for the number of terms in the sum be found

What are the methods or steps of drawing reciprocal lattice?

Can somebody explain me how can we visualise reciprocal lattice of a crystal lattice. Also what do we mean by wavevectors of a reciprocal lattice. What is its physical significance?

here is a question on reciprocal lattices that I am stuck on for a simple cubic lattice, the unit cell is defined by a1=a(1,0,0) a2 = a(0,1,0) a3 = a(0,0,1), demonstrate that the reciprocal lattice of its reciprocal lattice is the original crystal lattice.From what I've found, i think the...

Homework Statement Show that the reciprocal cubic of cubic lattice is also cubic. Homework Equations cos\alpha*=\frac{cos\beta cos\gamma-cos\alpha}{sin\beta sin\gamma} cos\beta*=\frac{cos\alpha cos\gamma-cos\beta}{sin\alpha sin\gamma} cos\gamma*=\frac{cos\alpha...

Hi, all I got a question about the origin of reciprocal space..what is the physical nature of the special point? Does that originate from diffraction? or Is that a diffraction points? We know that a 'normal' reciprocal point designates a group of parallel plane. How about the origin of...

I have seen this sort of thing over the past few years and it is bothering me, something like this \frac{ds}{dx}=\frac{1}{\frac{dx}{ds}} But it seems to me that this sort of thing only works in certain situations. For example, take s(x) to be s(x)=x^{2} so that \frac{ds}{dx}=2x Now to get...

I have need to calculate the residues of some functions of the form \frac{f(x)}{p(x)} where p(x) is a polynomial. To be more specific I have already calculated the 2 residues of \frac{1}{x^2+a^2}. That one was quite easy. Now I'm asked to calculate the residues of...

I am aware of the expectation value \left\langle\ r \right\rangle. But I was wondering what is physically meant by the expectation value: \left\langle\frac{1}{r}\right\rangle The reason I am asking is because calculating this (reciprocal) expectation value for the 1s state of hydrogen, one...

Homework Statement If A is nonsingular, prove that the eigenvalues of A-1 are the reciprocals of the eigenvalues of A. *Use the idea of similar matrices to prove this. Homework Equations det(I\lambda - A) = 0 B = C-1AC (B and A are similar, and thus have the same determinants) The...

Homework Statement https://www.physicsforums.com/attachment.php?attachmentid=21977&stc=1&d=1258886072 I think my proof is lousy and may be wrong. Please help me with it (= Thanks in advance Homework Equations My proof is of below. The Attempt at a Solution

Consider two groups of 3 spaceships each. The groups are numbered 1 and 2. The ships in group 1 are numbered 1A, 1B and 1C. The ships in group 2 are numbered 2A, 2B and 2C. In each group, ship A leads, followed directly in line, at fixed and equal proper intervals (as measured in each line's...

Hi, There are some points I really want to clear up in this topic...I promise to finish my chain of doubts as quicly as possible! I'll put in my first questions... 1. Rotoinversion is a combination of inversion and rotation-- often it ends up as having the same effect on the crystal as...

f(\vec{r}) = f(\vec{r}+\vec{T}) \vec{T}= u_{1} \vec{a_{1}} + u_{2} \vec{a_{2}}+u_{3} \vec{a_{3}} u_{1},u_{2},u_{3} are integers. f(\vec{r}+\vec{T})= \sum n_{g} e^{(i\vec{G}.(\vec{r}+\vec{R}) )}= f(\vec{r}) e^{i\vec{G}.\vec{R} }= 1 \vec{G}.\vec{R} = 2\pi m we call...

Is it possible to have the reciprocal of a cubic function that does not have any vertical asymptotes?

Homework Statement For the function y = 1 / ((x-1)^2) what is: a) the sign of slope b) change in slope (increasing or decreasing) for the interval x > 1 Here is the graph: http://img7.imageshack.us/img7/3204/12491454.jpg Homework Equations None The Attempt...

Homework Statement http://img97.imageshack.us/img97/1521/lastscano.jpg Homework Equations avg speed = distance / time The Attempt at a Solution not sure how to go about this one, looking for a few hints on how to get the equation. answer is : t = 3850 /v But I am not...

Homework Statement Given the shortest reciprocal lattice of fcc is (2PI/a)(+-x+-y+-z). How can i show that (111) is perpendicular to the shortest reciprocal lattice? And how to show that other planes such as (001),(010),(110) is not perpendicular to the shortest reciprocal lattice...

Why the name Reciprocal lattice ?? Is it because the dimensions get bigger & we are able to understand the structure on a macro level & removing the infinities that occur in h, k, l plane system ??

1. How to solve -1<1/(x+1)<2 2. Now if I switched both sign and took the reciprocal such as 1/-1>(x+1)/1>1/2 I get the right answer: x<-2 and x>-1/2. 3. Without using the reciprocal property would be lengthy and confusing, but I have very little and contradictory information found...

Homework Statement A road is built up the slope of a hill with a height of h meters and an angle of inclination of x. The length of the road is d. a) Sketch a diagram of this situation. Label all quantities. b) Show that the length of the road is represented by the relation d = h csc x. c)...

Hey folks, Here's my problem: Knowing that for reciprocal lattice vectors K and real space lattice vectors R: and using the Kronecker delta: I need to prove b1, b1, b3 as shown http://www.doitpoms.ac.uk/tlplib/brillouin_zones/reciprocal.php" : I understand that for the...

Homework Statement Why is parallel resistance the reciprocal of all individual resistances? Homework Equations V=IR The Attempt at a Solution Well, since V is constant and I is different, you can write it as I=V/R, and since V won't change, you can make it I=V*(1/R1+1/R2),etc...

I'm trying to build up enough understanding to work through some GR on my own, but I'm horribly confused by some of the math concepts. So terribly so, that I'm not even sure how to ask my questions. Please bear with me. Lets work in a 2D plane. Assume I have a vector u which I can write out...

Hi, I'm a college student in Singapore... Currently doing some research on carbon nanotubes, and so happened one of the honors student in the same lab said something about reciprocal lattice after seeing my experimental results. I went to search more about it, but i am totally clueless...

Homework Statement Let f(x) be defined by the following Fourier series for \left|x\right|: f(x) = \frac{\pi}{2} - \frac{4}{\pi}\sum_{1,3,...}\frac{cos\left(nx\right)}{n^{2}} Show that \sum_{1,3,...}\frac{1}{n^{2}} = \frac{\pi^{2}}{8} and \sum_{1,2,3,...}\frac{1}{n^{2}} =...

I am taking Solid State now and using Kittel as the textbook. Needless to say, I don't understand almost anything that's happening. I'm still stuck on Reciprocal Space here. If I have a lattice of atoms of spacing X, then in reciprocal space I get something like 2*pi/X spacing. My prof...

Homework Statement Let {a,b,c} be any basis set. Then the corresponding reciprocal {a*,b*,c*} is defined by a*=b x c/[a,b,c] , b*=c x a/[a,b,c], c*=a x b/[a,b,c] If {i,j,k} is standard basis, show that {i*,j*,k*}={i,j,k} Homework Equations The Attempt at a Solution I have...

Hello all, I don't understand some things concerning reciprocal space. I know how it appears from quantum mechanics (it comes from gas of free electrons model, then applying Fermi-statistics for it and solve Heisenberg equation and get some kx,y,z which have to be integer. After that we call the...

If there is a contravariant vector v=aa+bb+cc with a reciprocal vector system where [abc]v=xb×c+ya×c+za×b would the vector expressed in the reciprocal vector system be a covariant vector? Is there any connection between the reciprocal vector system of a covariant vector and a...

[SOLVED] Integral of Square of Reciprocal of √(a + cos t) Homework Statement Demonstrate that \int_0^\pi \frac{dt}{(a + \cos t)^2} = \frac{a\pi}{(\sqrt{a^2 - 1})^3} where a > 0. The attempt at a solution I want to compute this using the Residue Theorem. The first thing I did was...

Hello, can someone tell me the difference between reciprocal and the inverse. I have looked up the defenition and when I think I get a deep understanding I get confused. Thanks for all the help. Naicidrac

1. Find the antiderivative of 1/(x+3)^2 Okayy i knwo this is an easy problem but i COMPLETELY forget how to do it. Ive tried using partial fractions but it doesn't seem to be working. I just need to know how to start the problem then i should be alright from there. Thank you!

Homework Statement Here's a problem I'm having: The primitive vectors of the hexagonal lattice are: a1 = ck a2 = (a/2)i + ([a√3]/2)j a3 = (-a/2)i + ([a√3]/2)j Find the primitive vectors of the reciprocal lattice, i.e. b1, b2, and b3. Homework Equations I do know that the...

Hi, can anybody rigurously explain the relationship between the band diagram in k-space (I think I understand this one) and the diagram in real space (as is often used to explain the p-n-junction).

First off, this is not a homework problem. I was reading Charles Kittel solid states book on Chapter 2, equation 3: electron number density, n(x), expanded in a Fourier series: n(x) = n_0 + \sum_{p} [C_p cos(\frac{2\pi p x}{a}) + S_p sin(\frac{2\pi p x}{a})] From this expansion, wouldn't...

Problem: How do you determine the line of symmetry of a reciprocal equation? Solution: For example, I'll graph the reciprocal function Y=1/(x+2) ^Just a quick sketch And the equation of the line of symmetry is simply -(x+2), which can be seen here: ^Also a quick sketch By adding a...

reciprocal functions ?? hey is this true with finding reciprocal functions : f(x) initial function , g(x) reciprocal function of f(x) if f(x) = a x^n then g(x) = ( xroot(n, x) ) / ( xroot(n, a) but now if f(x) = ax²+ bx + c how do i find its reciprocal function ?

Homework Statement "What does a reciprocal lattice vector represent in the real lattice?" The Attempt at a Solution The answer to that one is that the reciprocal lattice represent all possible k-values for the incoming radiation to be contained in the real lattice. Hence a...

I have been learning kittel's solid physics, But find it hard to have a firm grab of what a reciprocal lattice is like and can't understand it's relationship with e original lattice.. Is there a picture that draws a lattice n its reciprocal lattice into e same picture? so that i can visualize...

Homework Statement Find the shortest reciprocal vector G, given below, v_1,...,v_3 are integers. \vec{G} = \frac{2 \pi}{a}\left( (v_2 + v_3 )\vec{x} + (v_1 + v_3 )\vec{y} + (v_1 + v_2 )\vec{z} \right) Homework Equations x,y,z are ortonogal, length 1 l = l(v_1, v_2, v_3) =...

Hi. I was just wondering, how can i prove the following identity: \frac{{dy}}{{dx}}\frac{{dx}}{{dy}} = 1 Its nothing that I am required to know, but i was just curious, so for all i know, it may be way out of anything that i can mathematically comprehend. The best I've been able to...

I understand that NaCl and NH4HCO3 are reciprocal salt pairs. What does this mean?

I am trying to understand 3D Si dispersion relations and reciprocal lattice vectors. My confusion is that when I look at dispersion relations the wave vector typically is normalized from 0 to 1 by a/2pi. I thought the edge of the first BZ was pi/a. Is this correct or is it 2pi/a for a diamond...

Homework Statement http://img412.imageshack.us/img412/4712/abcww1.jpg Homework Equations Using Compatibility Equation & Prinicipal of Superpositon to find Reaction force at C. Using Principal of Superposition and Maxwell Reciprocal Theorem, to find out Reaction force at C. State...