Normalization Definition and 229 Threads

I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67} The singular contribution...

When doing the standard procedure for normalisation a wavefunction, I get $$|A|=\sqrt \frac{2}{L}$$ where A is the normalisation constant. It is mathematically correct to say that $$A=\sqrt \frac{2}{L} e^{i\theta}$$ but would this be a valid answer for the normalisation constant? In my lecture...

Hi, when normalising the wavefunction I get two answers. Is this correct? My notes only has 1/sqrt(L) = A.

Consider the state ##\ket{\Psi} = \sum_{1 \leq n_{1} \leq n_{2} \leq N} a(n_{1},n_{2})\ket{n_{1},n_{2}}## and suppose $$|a(n_{1},n_{2})| \propto \cosh[(x-1/2)N\ln N]$$ where ##0<x=(n_{1}-n_{2})/N<1##. The claim is that all ##a(n_{1},n_{2})## with ##n_{2}-n_{1} > 1## go to ##0## as...

a and b were fairly easy to solve; but the c part which actually demands the probability! How are we suppose to fetch the value if the function can't even be normalized; I tried to make some assumptions like making the system bounded; but I don't think that it's the right way to do so... What...

Hi, this was one of the oral exam questions my teacher asked so i tried to solve it. Consider y>0 the energy spectrum here is continuous and non degenerate while for y<0 the spectrum is discrete and non degenerate because E<0. for y>0 i thought of 2 cases case 1 there is no wave function for...

If wave functions are individually normalized does it mean that they are also normalized if phi 1 and phi 2 are integrated over infinity?

I need to normalise F= Cexp(-r/a) To do this, I squared the integrand to get C^2exp(-2r/a). Then I integrated with infinite limits (from 0 to infinity) and equated to 1. The answer to the integral (confirmed by symbolab) is -a/2exp(-2r/a). When I set the limits I get sqrt(2/a). The book says the...

I don't really know where to begin. 1. idea: For a spatial wave funtion I'd have to calculate the integral over dxdydz for -inf to +inf. But that doesn't seem very reasonable to me here. $$\int \chi dxdydz=\int A\begin{pmatrix} 3i\\ 4 \end{pmatrix} dxdydz$$ Do have to substitute dxdydz with...

Can somebody explain why the kinetic term for the fluctuations was already diagonal and why to normalize it, the sqrt(m) is added? Any why here Z_ij = delta_ij? Quite confused about understanding this paragraph, can anybody explain it more easily?

I'm given the wavefunction and I need to find the normalization constant A. I believe that means to solve the integral The question does give some standard results for the Gaussian function, also multiplied by x to some different powers in the integrand, but I can't seem to get it into...

Hi everyone, I am struggling to understand whether the results of FMESH tallies are already divided by the cell volume or not. I'd actually expect so considering: 1. the comparison with an F4 tally in the same cell where results are comparable only if I assume that the mesh tallies results are...

Hello! I am trying to use the wavefunctions of a Morse potential as defined in the link provided. They define a parameter ##z## and the wavefunctions are in terms of z. In my particular case, given their definitions, I have ##\lambda = 132.19377##, ##a=1.318 A^{-1}## and ##R_e = 2.235 A##. I am...

What I have done is the following: \begin{equation} \braket{\eta_k | \eta_k}=|N|^2\sum_{n=0}^{\infty}\dfrac{1}{n!}\bra{0}(A^{\dagger})^nA^n\ket{0}=|N|^2\sum_{n=0}^{\infty}\dfrac{1}{n!}\int...

Hello, On the topic of feature scaling: I am wondering if normalization needs to be used all the time or only in some particular circumstances. Normalization means transforming/remapping the range of a variable with values ##[x_0,x_f]## to the range ##[0,1]##. For example, let's consider a...

I have attached my attempt and proof that my attempts were incorrect.

I ran into this question in my problem sheet. Does anybody know how to work it out?

Hello, there. Looking at the Einstein-Hilbert action $$S=\frac 1 {16\pi G}\int R \sqrt{-g}d^4 x,$$ I am wondering why the normalization constant is ##1/16\pi G##. In the textbook by Carroll, he mentions that the action is so normalized to get the right answer. I think this is related to...

Dear Community, I am having a question. I have developed a simple code to perform iteration power algorithm and find the keff value of a system. However, it is not still totally clear in my mind if I have to normalize all my scores by the eigenvalue, i.e. multiply by the keff (fluxes, power...

I tried writing the function as: Ѱ = c1Φ1 + C2𝚽2 + C3𝚽3 in order to then find mod C1^2... But ɸ = √2/a sin(ᴨx/a) and not sin(ᴨx/a) I cannot understand how the factor of "√2/a " comes

In Quantum field theory by Peskin Schroeder for relativistic normalization δ(p'-q')=δ(p-q) dp'3/dp3 where the boost is in z direction. How did they compute it?

Suppose ##I \subseteq k[X_{1}, X_{2}, X_{3}, X_{4}]## be the ideal generated by the maximal minors of the ##2 \times 3## matrix $$\begin{pmatrix} X_1 & X_2 & X_3\\ X_2 & X_3 & X_4 \end{pmatrix}.$$ I have to find a Noether normalization ##k[Y_1, Y_2, Y_3, Y_4] \subseteq k[X_1, X_2, X_3, X_4]##...

Im trying to solve the equation 62.7 of this numerical on mathematica. Whenever i try to normalized the function it shows function diverges. As the Bessel function contains trigonometry term so it diverges. I don't know how to solve the integral. Can i use the hydrogen atom wavefunction in exp...

I have been working with some time series data of spectral signals, each wavelength has a different signal, so I normalize the data so I can plot it effectively. However, I am struggling to quantify the new normalized data. I will give an example below. Normalizing data often refers to...

I've worked through it doing what I thought I should have done. I normalized the original wavefunction(x,0) and made it = one before using orthonormality to get to A^2(1-1) because i^2=-1 but my final answer comes out at 1/0 which is undefined and I don't see how that could be correct since A is...

I am working through David Griffiths' "Introduction to Quantum Mechanics". All of the solutions are provided online by Griffiths himself. This is Problem 2.5(e). I understand his solution but I'm confused about one thing. After normalizing Ψ, we find ##A=\frac {1}{\sqrt2}##. Griffiths notes that...

I do not know what I'm doing wrong but I'm working on the problem of finding the normalization constants for the energy eigenstate equation for a 1D plane wave that is traveling from the left into a potential barrier where E < V at the barrier. This is from Allan Adams' Lecture 12 of his 2013...

Hello! I have some data points generated from an unknown distribution (say a 1D Gaussian for example) and I want to build a neural network able to approximate the underlaying distribution i.e. for any given ##x## as input to the neural network, I want the output to be as close as possible to...

Should I treat ψ1 as ψ and ψ 2 as ψ*?

Homework Statement Find the noralization constant ##A## of the function bellow: $$ \psi(x) = A e^\left(i k x -x^2 \right) \left[ 1 + e^\left(-i \alpha \right) \right], $$ ##\alpha## is also a constant. Homework Equations ##\int_{-\infty}^{\infty} e^\left(-\lambda x^2 \right) \, dx = \sqrt...

Having read many times about normalizing quantum mechanics to agree with classical equations, can you please give an explanation or an example of the mathematics involved? I have looked in Wikipedia, but was unable to find anything. Maybe I am using the wrong keywords. Is there an article or an...

Homework Statement Determined wave function in a hydrogen atom. ## Ψ(r,θ,Φ) = A(x+iy)e^{ \frac{-r}{2a_0}}## << find A by normalization Answer of a question in my book is ## A = -\frac{1}{a_0 \sqrt{8 \pi}} (\frac{1}{2a_0})^{3/2} ## Homework Equations ## \int Ψ^*(r,θ,Φ)Ψ(r,θ,Φ) d^3r = \int \int...

Homework Statement The Fourier transfrom of the wave function is given by $$\Phi(p) = \frac{N}{(1+\frac{a_0^2p^2}{\hbar^2})^2}$$ where ##p:=|\vec{p}|## in 3 dimensions. Find N, choosing N to be a positive real number. Homework Equations $$\int d^3\vec{p}|\Phi(p)|^2=1$$ , over all p in the 3...

Hello all, I have a Radial Distribution Function in which the y-axis ie., g(r) value goes up to 40. But the other atoms values for g(r) are, say within 5. So when i plot these two it is difficult to see the smaller graph. So how do i normalize these value..?? I have attached an image. Any...

Homework Statement I have got the following matrix. I have found the eigen values but in some eq x, y & z terms are vanishing, so how to find the value of eigen vector? Also why we have to do normalization?? A__=__[1__1__0] ______[1__1__0] ______[0__0__1]Homework Equations A-λI=0 Ax = -λIx...

In the Wiki article on Montgomery's pair correlation conjecture https://en.wikipedia.org/wiki/Montgomery%27s_pair_correlation_conjecture, it is stated that the normalized spacing between one non-trivial zero γn =½+iT of the Riemann zeta function and the next γn+1 on the critical strip Re(z)= ½...

Say we have a difficult integral of the form ##\displaystyle \int_a^{b}f(x) ~dx##. Let ##t = \frac{x-a}{b-x}##. Then ##\displaystyle \int_0^{\infty}f \left( \frac{bt+a}{t+1} \right)\frac{1-a}{(t+1)^2} ~dt##. My idea is that making this change of variables transforms the integral into a form...

Homework Statement I have the wave function Ae^(ikx)*cos(pix/L) defined at -L/2 <= x <= L/2. and 0 for all other x. The question is: A proton is in a time-independent one-dimensional potential well.What is the probability that the proton is located between x = − L/4 and x = L/4 ? Homework...

Hi, Lets say I have N independent, not necessarily identical, random variable. I define a new random variable as $$Y=Σ^{N}_{i=0} X_{i}$$ does Y follow a normalized probability distribution?

Given two probability amplitude wavefunctions, one in position space ##\psi(r,k)## and one in wavenumber space ##\phi(r,k)##, where ##r## and ##k## are Fourier conjugates, how is it possible for the modulus squared, i.e., probability density, of BOTH wavefunctions to be normalized? It seems...

Homework Statement Show that the normalized wave function for a particle in a three-dimensional box with sides of length a, b, and c is: Ψ(x,y,z) = √(8/abc) * sin(nxπx/a)* sin(nyπy/b)* sin(nzπz/c). Homework Equations Condition for the normalization: ∫0adx ∫0bdy ∫0cdz Ψ*(x,y,z)Ψ(x,y,z) = 1...

I am trying to normalize 4x4 matrix (g and f are functions): \begin{equation} G=\begin{matrix} (1-g^2) &0& 0& 0&\\ 0& (1+f^2)& (-g^2-f^2)& 0 \\ 0 &(-g^2-f^2)& (1+f^2)& 0 &\\ 0& 0& 0& (1-g^2) \end{matrix} \end{equation} It's a matrix that's in a research paper (which I don't have) which gives...

Homework Statement Show that the (1,0,0) and (2,0,0) wave functions are properly normalized. We know that: Ψ(1,0,0) = (2/(a0^(3/2))*e^(-r/a0)*(1/sqrt(2))*(1/sqrt(2*pi)) where: R(r) = (2/(a0^(3/2))*e^(-r/a0) Θ(θ) = (1/sqrt(2)) Φ(φ) = (1/sqrt(2*pi)) Homework Equations (1) ∫|Ψ|^2 dx = 1 (2)...

Homework Statement State from the wavefunction: Ψ(x) = ∫(dk/2π) f(k) uk(x) Calculate the normalization <Ψ|Ψ> Homework Equations <Ψ|Ψ> = ∫|Ψ(x)|^2 dx The Attempt at a Solution [/B] Well I know the relevant equations, but I am not sure how to compute the integral in order to start...

Homework Statement [/B] Determine the value that A (assumed real) must have if the wavefunction is to be correctly normalised, i.e. the volume integral of |Ψ|2 over all space is equal to unity. Homework Equations Integration by parts (I think?) The Attempt at a Solution So, I've managed...

Homework Statement ## \psi(x) = N. (x^2 - l^2)^2 ## for ##|x| < l , 0 ## otherwise We have to find N such that this wavefunction is normalised.2. The attempt at a solution I tried expanding the ## (x^2 - l^2)^2 ## term inside the integral but this integral is extremely messy : ##...

IN Srednicki's QFT he seems to make two different choices for normalizing the generators of lie algebras. In chapter 24 (eqn 24.5) he chooses Tr (TaTb) = 2 δab and in chapter 69 (eqn 69.8) he chooses Tr (TaTb) = (1/2) δab Is there a reason for this? Is there any particular reason to make one...

What are the applications to normalize to 1? what is the difference between the integral of de function in all the space equal to 1 with normalize to 1?