Inversion Definition and 108 Threads

The notes my lecturer has provided state that the maximum temperature can be found taking p = 0 in the inversion curve formula, given as: I’m not sure how to obtain this?? These are the formulas: This is my attempt at a solution : Not sure if this approach is right?

I'm having trouble understanding stimulated emission and population inversion, and how they work together to make a laser work. I pretty much need this explained completely. 1. Spontaneous emission, they say, is when an atom absorbs and then later emits a photon. Isn't that just regular...

I would like to solve a system of systems of equations Ax=b where A is an n x m x p tensor (3D) matrix, x is a vector (n x 1), and b is a matrix (n x p). I haven't been able to find a clear walk-through of inverting a tensor like how one would invert a regular matrix to solve a system of linear...

Recently I've started reading Weinberg QFT, Vol 1, to introduce myself better to quantum field theory, after finishing courses in qft at the university. Reading through the second chapter, I've found myself confused by his treatment of degenerate multiplets in Appendix C. Here is the equations...

How do the Pauli spin matrices transform under an inversion ? I think I mean to say the 3 dimensional improper rotation which is just in 3 dimensional matrix notation minus the identity - so exactly how are the 2 dimensional Pauli spin matrices changed. And under a 180 rotation do the 'y' and...

I have equation system: x + y + z - a*k = 0 -b*x + y + z = 0 -c*y + z = 0 -d*x + y = 0 where: a, b, c, d = const. Have to find: x, y, z, k Attempt of solution: I create Matrix A with coefficients; Matrix B - Solutions (Zeros) and Matrix X - variables. When I try to use Cramer's rule -...

Hi everyone, I am working on matrix inversion and focusing on low-complexity method such as iterative method. Recently, I am interested to explore how particle swarm optimization (PSO) can be applied to do matrix inversion. Since I am very very new in PSO, I have no idea how to start my work...

I'm having hard time finding the center of inversion of cubic diamond structure. At first I thought (2,2,2) would be the center of inversion, but (1,1,3), (3,3,3), (1,3,1), (3,1,1) (i.e. four atoms inside the cube) are not centrosymmetric about (2,2,2).

Hi, I'm studying MOSFET in detail and I'm struggling to understand how the channel is formed in case of SOI Mosfet. For normal mosfet A positive Gate to source voltage attracts electrons from P substrate towards Gate and thus a channel is formed. But in case of SOI There is a buried Oxide...

Hello Can somebody explain for me what is the meaning of inversion symmetry in solids? and why does it breaks at the surface? and also why this inversion symmetry breaking leads to SOC(spin orbit coupling)? If somebody also know a document that explain this in full details(from A to Z) please...

Hi! So I'm studying Gover's Algorithm and I have this doubt: Does 'Phase inversion gate' grows exponentially? I mean, if I want to signal the one combination that is the answer, I must be able to represent all 2^N states, where N is the number of qubits in the system. How do I do this without...

Homework Statement Rewrite following sequence as double stranded molecule, with an inversion of the sequence between nucleotide 4 and 12. 5'-TCTCGCATGGTAGGT-3' Homework Equations none. The Attempt at a Solution [/B] I've read in the textbook that you take the section and rotate it 180...

what is inversion symmetry?

How would this operator be implemented physically if we had a quantum computer? In Grover's algorithm this magical operator is often called "phase inversion". Here is the operator from wiki: https://wikimedia.org/api/rest_v1/media/math/render/svg/07fb23bffa787430b084971c6a108a8f6ff6c2b3 It’s...

Mentor note: Split the thread in two parts, the other part is here: When (and Why) Does a Human Baby's Vision "Flip". This thread discusses the inversion of human vision, "up/down", "left/right" and 180 degree rotations. Greetings to all, I realize that there is another "dead thread" about this...

Hi. In thermodynamic equilibrium, the ratio between spontaneous and stimulated emission is $$\frac{A_{21}\cdot N_2}{B_{21}\cdot N_2\cdot u(f)}=e^{\frac{hf}{k_B T}}-1$$ where ##A_{21}## and ##B_{21}## are Einstein coefficients. This means, that there's always much more spontaneous than...

I was just wondering: why does lower kinetic temperature imply population inversion? I've read this is true in a few (astrophysics) texts regarding molecular clouds, although this seems to be a more general result that I haven't really read an entire explanation for. Nevertheless, do you have...

Homework Statement Let ##\left|\psi\right\rangle## be a non-degenerate stationary state, i.e. an eigenstate of the Hamiltonian. Suppose the system exhibits symmetry for time inversion, but not necessarily for rotations. Show that the expectation value for the angular momentum operator is zero...

If ##t## is a function of ##r##, then we may in theory find ##r## as a function of ##t##, as claimed in the last paragraph of the attachment below. My issue is this is only true if ##t## is a 1-1 function of ##r##. Otherwise, suppose ##t=r^2##. Then ##r=\pm\sqrt{t}##, which isn't a function. I...

The well known Euler angles (αβγ) are defined as in the image It is easy to see that under inversion α → π+α β → π-β but I cannot figure out how γ transforms under inversion. actually I am stuck at the question whether I should measure it from the same intersection line ON (thence γ →π+γ) or...

Hi everyone, I am new here. I am working in geophysics and I would like to invert for a simple layered velocity model using CMA-ES optimization method. I downloaded the purecmaes.m code in Matlab here: https://www.lri.fr/~hansen/cmaes_inmatlab.html, and also implemented one in Fortran 90. I...

I find in many textbooks that when expanding the crystal field in spherical harmonics, those terms of odd ranks do not appear in the expansion even if the crystal lacks an inversion centre such as the tetrahedral crystal field. Why is that? and when one should include spherical harmonics of odd...

When I plot the isenthalpic curves in T-P plane, I see isenthalpic curves are not well defined in the lower temperature region in T-P plane. Inside the inversion curve Joule-Thomson coefficient is positive so gas cools and outside of the inversion curve Joule-Thomson coefficent is negative so...

For my Quantum II class I am working on a paper about masers. I am using a naive model (a coupled pair of infinite potential wells), and I would like to find out where I can find a graph of the inversion potential energy curve. This would be a simple one dimensional curve of the potential...

Would it be possible to get a 1 degree of freedom (the saddle line of the potential energy surface) potential energy curve from the inversion of Ammonia from the software Avagadro (I have just started playing with this software yesterday)? I am doing a physics paper for a graduate QM class, and...

Hi, I'm doing a module on quantum optics and lasers. Most of the texts and online source I have read simply state that 'population inversion is essential for amplification in laser operation'. My question is, why? Amplification/Gain is essentially the result of stimulated emission. Can't...

Hello everybody! I'm sorry if it's not the right section to post in. I'm trying to solve this exercise: $$\frac{1}{2i\pi}*\int_{8-i\infty}^{8+i\infty}\frac{e^{s(t-5)}}{(s+4)^2}ds$$ The request is to find the result in function of $$t$$ I know i must use the Riemann inversion formula, and so the...

Noether's theorem said that because of homogeneity in time the law of conservation of energy exists. I am bit of confused and I am not sure is also time inversion some consequence of this. For example in the case of free fall we have symmetry ## t \rightarrow -t##. I am sometimes confused of...

Hi all. I have to do Fourer inversion of an equation 7.46 but I don't know how to do that. If anybody has any idea it wolud be very helpfull. Inversion of S(q) is G(r).

Do lightwaves experience wave inversion after striking a mirror?

Homework Statement Find the inverse of the matrix: 1 1 -1 2 -1 1 1 1 2 Homework Equations One must be aware of the identity matrix, as well as how add one row to another with matrix multiplication, for example, the matrix 1 0 0 k 1 0 0 0 1 would add k times the first row to the second...

First by antisymmetric tensor I mean the "totally antisymmetric tensor" like this: ##\epsilon^{\alpha\beta\gamma\delta} = \left\{ \begin{array}{clcl} +1 \;\; \text{when superscripts form an even permutation of 1,2,3,4} \\ -1 \;\; \text{when superscripts form an odd permutation of 1,2,3,4} \\ 0...

Hello I hope this is the right place to ask this question. For my thesis I need a way to invert a incomplete elliptic integral of the second kind. I believe the Jacobi elliptic functions are inverse of the elliptic integral of the first kind. The calculation I'm doing is symbolic so a...

I have some measurement data for known spectrum. Now I want to establish a algorithm for later measurement of unknown spectrum. I attached the equation in the image. r g b filters apply to the true spectrum I I am looking for. R G B are the measurement getting from the device. I1, I2, I3 are...

Homework Statement Consider two spin 1/2 particles interacting through a dipole-dipole potential \hat{V} = A\frac{(\hat{\sigma_1} \cdot \hat{\sigma_2})r^2 - (\sigma_1 \cdot \vec{r})(\sigma_2 \cdot \vec{r})}{r^5} If both spins are fixed at a distance d between each other, and at t = 0 one of...

Hello to experts! What is impedance inversion in quarter wave transformer? I need definition not a concept, not explanation, not description. But a precise and point definition. Thank you very much.

Hi I am unable to find the proof of the Lagrange inversion formula as given in http://en.wikipedia.org/wiki/Lagrange_inversion_theorem#Theorem_statement I have searched all over the internet as well as the original paper published by Lagrange. Still could not find it. Any help would be...

Homework Statement In order to achieve population inversion between two states that are separated by an energy difference of 3.5 eV, what wavelength of pumping should be used. Homework Equations Not sure. The Attempt at a Solution I have no idea where to start with this one...

1. P. Marder ever said that there is no special symmetry results in two dimensional oblique lattice. But it still possesses inversion symmetry. r → -r How to understand r → -r? 2. Many book ever states that space symmetry broken by atomic displacement can bring ferroelectricity. But why...

I would like to take an incoming signal (digital or analog), invert it, and send it to an antenna. What is a simple high-level approach to this?

Hi, I have a matrix that is nearly singular, so I am using singular value decomposition (SVD) approach for inversion. In this case an N-by-N matrix can be written as: \mathbf{H}=\mathbf{U}\Sigma\mathbf{V}^H Then the inverse can be written as...

hi,everyone. How to do Abel inversion using Matlab? what is the algorithm? I read something in wiki,but I have no idea how to perform it! anything helpful would be highly appreciated.

I am working on the following problem: Can someone please show or explain the steps to invert the phi matrix? I've given it a few tries, but I can't reach what the book has for the answer. Please help! Thanks

matrix inversion with complex numbers?? or faster way? Homework Statement The Attempt at a Solution i managed to get the answer, but it took me like 30min. to work this by hand. i probably worked it differently than my instructor's method above, but wat i did was get the coefficients of V...

I don't really know where this topic belongs. Let's say you're an ugly asymmetrical person, with your right hand much larger than the left. A 4th dimensional being removed you and "flipped" you in the 4th dimesion, then put you back. Would you come back with a large right hand...

Hi :) So I'm learning about lateral inversion in plane mirrors and it's a bit confusing. I think of it like this:- Suppose you had a clone of your self who is standing next to you and facing the same direction. He walks a few steps forward and then turns to face you. When he turns to face...

Homework Statement For a gas obeying Dieterici's equation of state: P(V-b) = RTexp(-a/RTV) for one mole, prove that the equation of the inversion curve is P = ((2a/b^2) - (RT/b)) * exp((1/2) - (a/(RTb))) and hence find the maximum inversion temperature.Homework Equations N/A The Attempt...

I am unable to find any source describing at any lengths transformations of the type x \rightarrow -x beyond the case of static spacetime (and even in the case of static spacetime, it is rarely the fundamental definition, which tends to be more along the lign of orthogonality with an...

Homework Statement Hi guys, I'm trying to prove that matrix inversion is continuous. In other words, I'm trying to show that in a normed vector space the map \varphi: GL(n,R) \to GL(n,R) defined by \varphi(A) = A^{-1} is continuous.Homework Equations The norm that we're working in the...