# What is Normalization: Definition and 242 Discussions

Database normalization is the process of structuring a database, usually a relational database, in accordance with a series of so-called normal forms in order to reduce data redundancy and improve data integrity. It was first proposed by Edgar F. Codd as part of his relational model.
Normalization entails organizing the columns (attributes) and tables (relations) of a database to ensure that their dependencies are properly enforced by database integrity constraints. It is accomplished by applying some formal rules either by a process of synthesis (creating a new database design) or decomposition (improving an existing database design).

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1. ### Normalising the wavefunction - two answers

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

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...
3. ### Probabilities out of non-normalizable functions?

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...
4. ### Given the potential find the eigenfunction

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...
5. ### I Normalization of wave functions

If wave functions are individually normalized does it mean that they are also normalized if phi 1 and phi 2 are integrated over infinity?
6. ### I I cannot normalise this: F= Cexp(-r/a)

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...
7. ### Normalization of electron Spin state

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...
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### A Lagrangian: kinetic matrix Z_ij and mass matrix k_ij

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?
9. ### Help Solve for the normalization constant of this QM integral

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...
10. ### MCNP6.2 - Are results of FMESH tallies already divided by cell volume?

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...
11. ### A Normalization of Morse potential wavefunctions

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...
12. ### QFT: Normalization of coherent states

What I have done is the following: \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...
13. ### I Variable Normalization for different variable ranges....

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...
14. ### Infinite potential well problem normalization

I have attached my attempt and proof that my attempts were incorrect.
15. ### How do I normalize a wavefunction with Cn instead of Ci and Cj?

I ran into this question in my problem sheet. Does anybody know how to work it out?
16. ### I Normalization Constant in Einstein-Hilbert Action

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...
17. ### Neutron quantity normalization in an eigenvalue computation

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...

19. ### Normalization of a wavefunction

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
20. ### A Calculating Boosted Relativistic Normalization in Quantum Field Theory

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?
21. ### A How Do You Apply Noether Normalization to a Polynomial Ring Ideal?

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]##...

23. ### A Normalization of the radial part of the spherical harmonics

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...
24. ### B Normalization versus Percent Change

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...
25. ### Normalization constant A of a harmonic oscillator

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...
26. ### What are the coefficients of psi_n for this state?

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...
27. ### I Asymptotic normalization coefficient of a deuteron

Hello, I have been having trouble finding the ANC for the deuteron in the ground state and am wondering if someone knows where to find it? Thank you.
28. ### I Finding Normalization Constants for a Set of Energy Eigenstates

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...
29. ### Normalization condition with a neural network

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...
30. ### Probability of being in a state is given, Find the normalised wavefunction

Should I treat ψ1 as ψ and ψ 2 as ψ*?
31. ### Find the normalization constant ##A##

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...
32. ### I Mathematics of Normalization in Physics

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...
33. ### Wave function in a hydrogen atom : normalization

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...
34. ### Normalization of the Fourier transform

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...
35. ### A Normalization of Radial Distribution Function

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...
36. ### Normalization & value of Eigenvectors

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...
37. ### I Normalization of spacings

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...
38. ### I Normalization of integral bounds

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...
39. ### Normalization of wave function

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...
40. ### A Sum of independent random variables and Normalization

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?
41. ### I Normalization and the probability amplitude

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...
42. ### Normalization constant for a 3-D wave function

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...
43. ### A Is Normalizing a 4x4 Matrix Possible Using Multiple Methods?

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

### Show that the Hydrogen wave functions are normalized

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)...
45. G

### How Do You Normalize the Wavefunction Ψ(x) in Quantum Mechanics?

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...
46. B

### Normalization of Wavefunction Integration

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...
47. ### Finding Normalization constant

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 : ##...
48. ### A Srednicki's normalization choice for lie algebra generators

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...
49. ### I How to select a normalization method?

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?
50. ### I Constraints on potential for normalizable wavefunction

We know that in one dimension if ##E>V(\infty)## or ##E>V(-\infty)## then the resulting wave function will not be normalizable. The basic argument is that if ##E>V(\infty)##, then a stationary solution to the Schrodinger equation will necessarily have a concavity with the same sign as the...