Reciprocal Definition and 166 Threads

Hello ! I have read several threads on this topic but I don't seem to fully understand the reason for using the reciprocal space in crystallography . Can anyone please provide more information on this subject ?

So i don't really understand why the change in momentum of a crystal involves a reciprocal lattice vector. Surely it is just the change in momentum due to the change in the number and frequency of the phonons before and after whatever event/scattering/collision takes place. Can somebody please...

Hello, I was recently browsing the thread, http://mathhelpboards.com/challenge-questions-puzzles-28/evaluate-1-1-1-b-1-b-1-c-1-c-12074.html And I was browsing both, Kaliprasad's method and anemone's method. Lets take Kaliprasad's approach first. My question is about the reciprocal zeros...

Hi all, I'm curious about why reciprocal space is called precisely that. I always understood the reciprocal to be a word used in mathematics to describe the inverse or one divided by a number so how does that relate to frequency space unless in this case it means something completely...

Homework Statement This is from Cahill's Physical Mathematics. Exercise 5.23. For a \gt 0 and b^{2} – 4ac \lt 0, use a ghost contour to do the integral \int^{\infty}_{-\infty} \frac{1}{ax^{2}+bx+c} \mathrm{d}x Homework Equations Use contour integration and the residue theorem...

Homework Statement (a) For the delta-function potential and with P<<1, find at k=0 the energy of the lowest energy band. (This is part A of Charles Kittel Solid State Physics problem 7.3) Homework Equations (P/Ka)sin(Ka)+cos(Ka)=cos(ka) (note, K and k are different variables) ε=\hbar...

For a given lattice, specifically a diamond, it has C3v symmetry and the symmetry operation in real space is easy to see, 2C3 around high symmetry axis and 3sigma_v. My question is, if the lattice is expressed in reciprocal space, (say wavefunction defined in momentum space), then how to define...

If: \vec{v}=\frac{\mathrm{d} \vec{r}}{\mathrm{d} t} so: \\ \vec{v} = \frac{d\vec{r}}{dt} \\ \\ \vec{v}\;dt = d\vec{r} \\ \\ dt = \frac{d\vec{r}}{\vec{v}} \\ \\ \int dt = \int \frac{d\vec{r}}{\vec{v}} \\ \\ t = \int \frac{d\vec{r}}{\vec{v}} Is true? Solving the equation for time t, is need...

Digital signal processing -- conjugate reciprocal of a complex number what is the difference between conjugate of a complex number and conjugate reciprocal of a complex number i am asking with reference to z transform...Thanyou

Hello, I have some data that I am looking into correlation factors (Pearson). Let's say I have two data sets: X and Y. I have Graph X vs. Y then graph 1/X vs. Y. The reciprocal (1/X) yields a more linear relationship. Why does this occur? Thanks in advance!

This came up when I was trying to evaluate to a decimal value an arcsec(something), but on TI-83 there is no inverse secant button. So, I punched 1/(arccos(something)). Naturally, this came up as a domain error. Then my instructor pointed out arcsesc is not 1/arccosx. Oops. Thinking about...

Homework Statement Si(001) has the following lattice vectors in a (2x1) reconstruction \vec{a'_1} = \vec{a_1} + \vec{a_2} \vec{a'_2} = -0.5 \vec{a_1} + 0.5 \vec{a_2} Calculate the reciprocal lattice vectors of the reconstructed unit cell, \vec{b'_1} and \vec{b'_2} in terms of...

if dX/dY is the rate of change of X with respect to Y say that dX/dY = 3 now would it be correct if i say that the rate of change of Y with respect to X = 1/3 = dY/dX ?

I have just started diving into tensor analysis. To be honest, I didn't know whether to post this question in the vector analysis forum or this one. I have looked at a few books on the subject and scoured the internet, but I can't seem to find anything that answers this question. Or, maybe I...

Hi Everybody, I am learning solid state physics using a German book called "Festkorperphysik" written by Gross and Marx. Now, in page 336 the Schrodinger equation in momentum space is introduced: \left( \frac{\hbar^2 k^2}{2m} - E \right) C_\vec{k} + \sum_\vec{G} V_\vec{G}...

Hi, I have a question regarding reciprocal space symmetry operations and would appreciate if somebody can answer that: Lets say I have two k points, k1 and k2, in reciprocal space which are symmetric to each other. Since these two kpoints are symmetric to each other phonon scalar...

i have been searching for this but can't find a satisfactory answer

I got a bunch of questions about reciprocal lattice, I start with this one: In an x-ray experiment: For one specific orientation of your incident beam on your real lattice, only a portion of the points of your reciprocal lattice will become visible as your diffraction pattern right? See my...

How do I even represent the u's in indicial notation since the u's are labeled 1,2,3? I can't have components 1,2,3 and say u is $u_i$. With respect to the triad of base vectors $\mathbf{u}_1$, $\mathbf{u}_2$, and $\mathbf{u}_3$ (not necessary unit vectors), the triad $\mathbf{u}^1$...

As per Maxwell reciprocal theorem, it is valid only for elastic materials and structures indergoing small displacements.That is k12 = k21, kij = kji hence stiffness matrix is symmetric. Howbver, I just have been going through MY OWN written programs for geometric non linear problems and I...

Hello everyone, I have some conceptual issues with aforementioned definitions. How is exactly multiplicative inverse defined? Say, for a rational, nonzero number a/b, its reciprocal is b/a. Is there a certain operation that transforms a/b to b/a? Also, the notation for multiplicative...

Is this interesting? I have a way to represent all of the real numbers with a subset of the open interval (0,1). I write as a binary decimal x = .a_{0}a_{1}a_{2}a_{3}... where x = \sum -1^{a_{0}+1}/p_{i} where p_{i} is the i^{}th prime. Since the reciprocals of the primes diverges, in this...

Homework Statement The problem basically asks to solve the system x'(3x-1)=36e^{6t} by using laplace transforms.The Attempt at a Solution I've started by writing it (3x-1) = \frac{36e^{6t}}{3x-1} then applying laplace transform to the left side is quite simple, we get 3X(s) - 1/s. As...

According to the wikipedia entry, the latest values for the Lambda-CDM model parameters for the age of the Universe, t_0, and the Hubble constant, H_0 are t_0 = 13.75 \pm 0.11 \times 10^9 \mbox{ years} H_0 = 70.4 \pm 1.3 \mbox{ km s}^{-1} \mbox{Mpc}^{-1} If you combine the errors this implies...

After a long summer, I finding my new C3 homework a bit tricky, so any help would be great! Here is the question: sec(θ-150 degrees)=4 (solving for theta is greater than or equal to -180, but less than or equal to 180) So I know that sec is the reciprocal of cos so I changed the equation to...

Homework Statement The y = f(x) is the original graph. The question asks me to draw the y = 1/f(x) of that graph. What I did was just use the same x coordinates and then take the y coordinates and just do 1/y coordinate for each y coordinate. Is this the correct way to do it? Also, the red...

I am studying Solid state physics from kittel and I am stuck at the following equation. I can see that the exponential term turns to the kroneckler delta, but I don't understand how the integral gives the volume of the specimen, Ω? What am I not seeing? ∫d3x f(x)eiK.x = \sum aG∫d3x ei(K+G).x =...

Homework Statement Hi guys, I don't reach the correct answer to an exercise. I'm following Ashcroft's book. I must find that the reciprocal of the bcc Bravais lattice is a fcc one and the reciprocal of the fcc Bravais lattice is a bcc one. Homework Equations If a_1, a_2 and a_3 are...

Hello, I am having a hard time understanding the concept of the reciprocal space. Here is my general understanding of it so far: the reciprocal space contains all of the points that light could be diffracted to from the real space. But I don't understand why this is the case from the...

Homework Statement Evaulate the integral of (4-x2)-3/2.Homework Equations integration by parts u-replacement The Attempt at a Solution Too long to write it all down, but I used the aforementioned equations. Basically, I'd like somebody to give me a hint about how or where to start, since...

Hi, I am currently trying to model a set of data using a reciprocal function. I picked a couple of points, substituted the y and x values into two equations but I can't solve it! Here is an example: y = A / (Bx) 30 = A / (4.5B) 0.1 = A / (20B) I tried solving it by all methods I...

How can I help my students to comprehend/understand the concept of reciprocal lattice (pictorially) and Brillouin zone?

Homework Statement a 2d oblique lattice is described by the following vectors: a = 3i b = 0.5i + j sketch the unit cell of this lattice Sketch accurately the reciprocal lattice of the cell and justify the direction and relative magnitudes of each reciprocal lattice vector The...

can anyone tell me why we use reciprocal lattice for understanding the diffraction of X rays from crystal? thanks in advance :)

Hi all Sorry for reposting, the previous post wasn't clear enough, it's my mistake, I'll make the question more clear, I found lot of people asking the same question on the Internet. Given that X is random variable that takes values: 0.....H-1 The PMF of X is unknown, but I can tell...

Hi, I have an assignment where we basically have to make a Velocity vs. Substrate plot and find the Km and Vmax values. We then have to do a double reciprocal plot and find the Km and Vmax from that. My first question is if I have to convert the units of my axes so they are uniform...

From dirac, if A=B, then \frac{A}{x}=\frac{B}{x}+c\delta(x) (1) How this formula is derived? Since \frac{dlnx}{dx} = \frac{1}{x}-i\pi\delta(x) We can get \frac{A}{x} = A\frac{dlnx}{dx}+Ai\pi\delta(x) \frac{B}{x} = B\frac{dlnx}{dx}+Bi\pi\delta(x) So if A=B, \frac{A}{x}=\frac{B}{x}...

Homework Statement If g(x) is one-to-one and differentiable at every point in R, then its reciprocal 1/g(x) is also differentiable at every point in its domain. True of False? Homework Equations The Attempt at a Solution I have tried several times, and the statement seems to be...

From dirac, if A=B, then \frac{A}{x}=\frac{B}{x}+c\delta(x) (1) How this formula is derived? Since \frac{dlnx}{dx} = \frac{1}{x}-i\pi\delta(x) We can get \frac{A}{x} = A\frac{dlnx}{dx}+Ai\pi\delta(x) \frac{B}{x} = B\frac{dlnx}{dx}+Bi\pi\delta(x) So if A=B, \frac{A}{x}=\frac{B}{x}...

Homework Statement I have a function, y = 6*e^0.4x. How would I convert the regular form, y=a*e^bt to the form y= at^b? Homework Equations y = 6*e^0.4x The Attempt at a Solution I've tried to take the log of both sides, but if I do that, then "y" becomes a log, and I can't...

How do i prove that a reciprocal lattice vector G, where G= hb1+kb2+lb3 is perpendicular to a plane hkl in a crystal lattice? Is there Fourier involved?

How can i develop a sketch of the lattice and reciprocal lattice from vector form a=i+4j b=3i i know how to draw the wigner site cell, but I am having problems developing a sketch from vectors. what is the method for working it out..please help

I'm trying to get something straight. The multiplicative inverse or reciprocal is y=1/x, suggesting you just flip one to get the other. Can that numeral 1 sometimes be any number (in which case you're no longer flipping it) and still be a reciprocal? Using the relationship between heart rate...

How to prove that two reciprocal basis are either both right ended or both left-handed? If (e_1,e_2,e_3) and (e^1,e^2,e^3) are two such basis, since the scalar triple products depend on orientation, it would be enough to show that VV'=1 (where V and V' are the volumes, taken with their sign, of...

Reciprocal lattice? Hi everybody... I'm read about the band structure and the dispersion curve,I've got informations about the reciprocal lattice and how we determine it, but what I want to know why we use the reciprocal lattice in band structure calculations? thanks

Homework Statement For the angle shown a point is given on its terminal arm. Calculate the values of the three reciprocal trigonometric ratios, accurate to 4 decimal places if necessary. below is the link of the picture referring to the question https://www.virtualhigh...

Homework Statement The proof seems fairly straight forward, but after plugging in the primitive vectors to the equations for the reciprocal lattice vectors, I'm getting 2\pi\frac{\frac{a^2}{4}(x+y-z)}{\frac{a}{2}(y+z)\cdot(\frac{a^2}{4}(-x+y+z))} One proof I checked said that the bottom...

Hi, For an experiment I have a value for the error in time t (s) to be +-0.13s but I'm having difficulty getting from this to an error in t^-2 for the error bars drawn onto a graph. My values for t are in the range 36.84 - 24.88seconds. The range for t^-2 is 0.0007368 - 0.0016155 s^-2...

Can anyone help me find the reciprical coordinates of the K and M points in a simple hexagonal brilloiun zone? I have the lattice vectors and the reciprocal vectors, but I can't get the right coords (in recip coords) for the K point (the corner of the hexagon) and the M point (half way between 2...

at page 174 there is a result for kronig penney model in reciprocal space whic equals 1/a when i tried to it i am obtaining 1+1/a with mathematice so what is wrong do you know how to evaulate in more detail??how to obtain 1/a?? thx