What is Normalization: Definition and 241 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. schrodingerscat11

    Derivation: Normalization condition of Legendre polynomials

    Greetings! :biggrin: Homework Statement Starting from the Rodrigues formula, derive the orthonormality condition for the Legendre polynomials: \int^{+1}_{-1} P_l(x)P_{l'}(x)dx=(\frac{2}{2l + 1}) δ_{ll'} Hint: Use integration by parts Homework Equations P_l=...
  2. U

    Wavefunction Normalization at Different Times

    In Introduction to Quantum Mechanics by Griffith, when he is normalizing a wave function that's dependent on both x and t, he let's t=0 , and solves for the constant (A). But if the integration of ψ^2 at any time t is 1, then is it correct to let t = 2, for instance, instead of 0 and solve for...
  3. W

    Problem with normalization wave function position/momentum space

    Homework Statement We start with a pure state at t=0 of an electron is C e^{- a^2 x^2} \left(\begin{array}{c} 1\\ i \end{array}\right) Probability density of measuring momentun p_0 and third component of spin - \frac{\hbar}{2} And probability of measuring a state with momentum...
  4. J

    Normalization of the infinite square well.

    I have been going through my textbook deriving equations in preparation for my test on QM tomorrow. I noticed in the infinite square well that i was unable to complete the normalization. My textbook, Griffiths reads : (integral from 0 to a) ∫|A|^2 * (sin(kx))^2 =|A|^2 * (a/2) =1 Therefore...
  5. M

    I have a question about normalization of data

    Hello, please help me with this problem. The question is in the picture (LOOK AT THE ATTACHMENT). I don't know how to normzalize the data. How to know which method should be used? I need two methods of normalization here. HELP! Please teach me in detail. You don't have to give me the...
  6. A

    MHB Data Normalization Methods: Understanding and Choosing the Right One

    Hello, please help me with this problem. The question is in the picture. I don't know how to normzalize the data. How to know which method should be used? I need two methods of normalization here. HELP! Please teach me in detail.
  7. B

    Quantum Mechanics particle in Box Normalization

    Homework Statement A particle confined to a cubic box of dimension L the wavefunction normalization factor is (2/L)^3/2 , the same value for all stationary states. How is this result changed if the box has edge lengths L1, L2, L3, all of which are different. Homework Equations...
  8. J

    Quantum mechanics, free particle normalization question

    Homework Statement A free particle has the initial wave function ψ(x,0)=Ae^(-a|x|) Where A and a are positive real constants. a) Normalize ψ(x,0) Homework Equations 1= ∫|ψ|^2 dx The Attempt at a Solution I attempted to normalize using 1= ∫|ψ|^2 dx from -∞ to ∞. When...
  9. ShayanJ

    Normalization of Bessel functions of the first kind

    Before stating the main question,which section should the special functions' questions be asked? Now consider the Bessel differential equation: \rho \frac{d^2}{d\rho^2}J_{\nu}(\alpha_{\nu m} \frac{\rho}{a})+\frac{d}{d\rho}J_{\nu}(\alpha_{\nu m} \frac{\rho}{a})+(\frac{\alpha_{\nu m}^2...
  10. B

    Normalization of Orthogonal Polynomials?

    The generalized Rodrigues formula is of the form K_n\frac{1}{w}(\frac{d}{dx})^n(wp^n) The constant K_n is seemingly chosen completely arbitrarily, & I really need to be able to figure out a quick way to derive whether it should be K_n = \tfrac{(-1)^n}{2^nn!} in the case of Jacobi...
  11. T

    Normalization of Linear Superposition of ψ States

    Homework Statement An electron in an infinitely deep potential well of thickness 4 angstroms is placed in a linear superposition of the first and third states. What is the frequency of oscillation of the electron probability density?Homework Equations E=hωThe Attempt at a Solution My main...
  12. I

    Is the Airy Function Normalized?

    Is the Airy function (of the first kind) normalized? If I take the integral Ai(x) dx on the entire axis, does it converge to 1? I can't find this property by googling around :(
  13. K

    How is the √2 factor used in normalizing Qbit vectors?

    Homework Statement I'm a chemist, so forgive me. I'm looking at Leonard Susskind's course on 'Quantum Entanglement', and we've just started on Qbits. Electron spin: we have two column vectors (1,0) and (0,1) to represent the two states, call them 'up' and 'down'. The vector for the...
  14. G

    Proving Completeness Relation for Box Normalization

    In one dimension the normalized momentum eigenstate for a particle with periodic boundary conditions of length L is: \psi_k(x)=\frac{1}{\sqrt{L}}e^{ikx} . Is the completeness relation obvious: \Sigma \psi_k(x)\psi_{k}(0)=\frac{1}{L}\Sigma e^{ikx}e^{-ik0}=\frac{1}{L}\Sigma e^{ikx}=\delta(x)...
  15. phosgene

    Normalization of a symmetric wavefunction

    Homework Statement I need to find the normalization constant N_{S} of a symmetric wavefunction ψ(x_{1},x_{2}) = N_{S}[ψ_{a}(x_{1})ψ_{b}(x_{2}) + ψ_{a}(x_{2})ψ_{b}(x_{1})] assuming that the normalization of the individual wavefunctions ψ_{a}(x_{1})ψ_{b}(x_{2}), ψ_{a}(x_{2})ψ_{b}(x_{1}) are...
  16. Rorshach

    Normalization of wave function and estimation of values

    Homework Statement Hello, I have this problem with seemingly simple process, but there are things I either don't know, or make some stupid mistake on the way over and over. Here's the problem: At a particular time given by the wave function ψ(x)=N*x*exp(-(x/a)2) Determine N so that the wave...
  17. P

    MHB Geometric meaning of Noether normalization theorem

    Let $X\subset \mathbb{A}^n$ be an affine variety, let $I(X)=\{f\in k[X_1,\ldots,X_n]:f(P)=0,\ \forall P \in X\}$. We consider the ring $$A=k[a_1,\ldots,a_n]=\frac{k[X_1,\ldots,X_n]}{I(X)}$$ where $a_i=X_i \mod I(X)$.Noether normalization says that there are algebraically indipendent linear forms...
  18. L

    Normalization of SU(N) Group Generators

    I am reading my textbook of QFT (Maggiore, Modern Introduction in QFT), and there is this statement: "If T^a_R is a representation of the algebra and V a unitary matrix of the same dimension as T^a_R , then V T^a_R V^\dagger is still a solution o the Lie algebra and therefore provides...
  19. S

    Determining the normalization constant C

    Homework Statement Consider the distribution function F(x) = Cexp(-ax) Find the normalization constant C Homework Equations The Attempt at a Solution This is more clarification since this is not actually a homework problem but was in my profs notes. He started with the...
  20. Q

    Quantum Mechanics: The First Step in Proving the Constancy of a Normalization

    Homework Statement This is a much more general question regarding differential equations; however, since it was presented in a quantum mechanics text (and physicists often make appeals to empirical considerations in their mathematics), I thought it might be appropriate to post here. The...
  21. M

    Normalization of photon pulse. I'm confused

    Hi, Let's say I have a creation operator that creates a photon in some spatial mode. It has a spectral distribution given by f(\omega_{k}) So we have \mid 1_{p} \rangle=\int d\omega_{k}f(\omega_{k})a^{\dagger}_{k}\mid 0 \rangle Normalization implies that \int d\omega_{k}|f(\omega_{k})|^{2}...
  22. A

    Finding the Normalization Constant of a Gaussian Distribution (Griffiths 1.6)

    Homework Statement Consider the Gaussian Distribution ρ(x) = A e^{-λ(x-a)^{2}} where A, a, and λ are constants. Determine the normalization constant A. Homework Equations \int^{∞}_{-∞}ρ(x) dx = 1 The Attempt at a Solution The problem recommends you look up all necessary integrals, so I...
  23. T

    Normalization of step potential eigenfunction

    Hi, I am stuck with a problem which effectively boils down to this: Given the eigenstates of a Hamiltonian with a step potential in the x direction H=-\hbar^2/2m \nabla^2 + V_0 \Theta(x) \psi(q)_{in}=cos(qx)-\frac{\sqrt{K_{V_0}^2-q^2}}{q}sin(qz) \qquad x<0...
  24. S

    Normalization of wave function (Griffiths QM, 2.5)

    Homework Statement A particle in the infinite square well has its initial wave function an even mixture of the first two stationary states: \Psi(x,0) = A\left[ \psi_1(x) + \psi_2(x) \right] Normalize \Psi(x,0). Exploit the orthonormality of \psi_1 and \psi_2 Homework Equations \psi_n(x) =...
  25. O

    Theoretical impulse response and its normalization

    greetings, helpful people around the world, we all have heard once in our lives that the signal that is measure from your instrument, be it a spectrometer, optical microscope or an NMR machine, is not the real signal distribution, but the convolution of the real signal with an instrument...
  26. W

    Quantum Theory: Minimizing Energy Subject to Normalization Contraint

    Homework Statement In a previous problem, I derived that for a given wavefunction \Psi (x) in a potential, the energy of the state could be calculated as a functional of the wavefunction. I now need to minimize the energy, subject to the usual wavefunction normalization constraint, and show...
  27. J

    Finding the normalization constant for a 1-D time independent wave function

    Homework Statement ψ(x)=A((2kx)-(kx)^2) 0≤X≤2/k ψ(x)=0 everywhere else I need to find A Homework Equations ∫|ψ(x)|^2 dx=1 so I know I need to evaluate it between 0 and 2/k The Attempt at a Solution My problem is do I square the whole ψ(x)? If some one could point me in right direction I...
  28. D

    Normalization of a quantum particle

    Homework Statement Why is it important for a wave function to be normalized? Is an unnormalized wave function a solution to the schrodinger equation? Homework Equations ∫ ψ^2 dx=1 (from neg infinity to infinity) The Attempt at a Solution So I know normalization simply means that...
  29. M

    Understanding Normalization Factors in Scientific Research

    How is it that: See figure: Given: See figure too In details, I don't get the maths and simplification that took place! Thanks!
  30. J

    Normalization to delta distribution

    Do you know some example of an operator, other than momentum or position, that has (at least partially) continuous spectrum with eigenvalues s, and the corresponding eigenfunctions obey (\Phi_s,\Phi_s') = \int \Phi_s^*(q) \, \Phi_{s'} (q)~ dq = \delta(s-s')~? EDIT For example...
  31. S

    Normalization of ψ(x,0) - Can you tell me if my solution is correct?

    We are given ψ(x,0) = A[ψ1(x)+ψ2(x)] and for the first part of my homework problem it asks us to normalize ψ(x,0) (it says find A). What I did was ∫|ψ(x,0)|^2 dx = 1 = (|A|^2)∫(ψ1^2 + 2ψ1ψ2 + ψ2^2)dx and since ∫ψm(x)*ψn(x)dx = 0 when m≠n and it equals 1 when m=n I can make the integral equal...
  32. A

    Normalization of Radial wavefunction of hydrogen atom

    All I need to evaluate the normalization coefficient. I need a step by step guide. It will be a great help if someone please tell me where can i get the solution (with intermediate steps). I think the solution can be done using the orthogonal properties of associated Laguerre polynomial. I need...
  33. A

    Normalization Constant for Gaussian

    Homework Statement Find the normalization constant N for the Gaussian wave packet \psi (x) = N e^{-(x-x_{0})^{2}/2 K^{2}} Homework Equations 1 = \int |\psi (x)|^{2} dx The Attempt at a Solution 1 = \int |\psi (x)|^{2} dx = N^{2} \int e^{-(x-x_{0})^{2}/K^{2}} dx Substitute y=(x-x_{0})...
  34. R

    Image normalization and standardization

    Hi, I have a problem concerning MRI image normalization and scaling data between 0 and 1. I have three tissue classes with different intensity range on a set of images (intensity range for each tissue is varying from image to image): for one image for instance I have: GM (100-150), L(0-150)...
  35. K

    Quantum mechanics: Normalization and the width of distribution

    1. Homework Statement [/b] Normalize the following wave function, obtain the corresponding function in position-space (fourier transform) and find the width of the distribution in the x variable. Homework Equations \phi(p_x) = \begin{cases} 0, & \;\; |p_x-p_0| > \gamma \\ C, & \;\...
  36. Z

    Understanding Normalization in Gaussian Inputs

    what does normalization mean? for example say i have the guassian input as : A(0,T) = \sqrt{Po}*exp(-T^2/2To^2) then we can normalize it by defining t=T/To and A(z,T) = \sqrt{Po}U(z,t) Po= peak power t= normalized to the input pulse width To. if the peak of the pulse is...
  37. B

    What happens to normalization of wavefunction when you add a perturb correction?

    Homework Statement Consider any ket. Find the perturbative correction to that ket. Then, |n> = |n0> + |n1> Here, |n0> is the ket from the unperturbed hamiltonian (who cares what it is), and |n1> is the 1st order correction. Do you introduce a new normalization when you add the...
  38. W

    Time dependent wave function normalization

    Homework Statement Below is a wave function that is a linear combination of 2 stationary states of the infinite square well potential. Where ψ1(x) and ψ2(x) are the normalized solution of the time independent Schrodinger equation for n=1 and n=2 states. Show that the wave function is...
  39. K

    Normalization of vacuum state.

    It just occurred to me what if the vacuum state is not normalizable? We usually have the normalization \langle0|0\rangle=1, it's acceptable if we are sure the norm of vacuum state is always finite. However, we know states with definite momenta are normalized to delta functions, then how can we...
  40. F

    Normalization Conditions of Wave functions

    I am currently reading through Griffiths Quantum Mechanics textbook, and on page 14, Griffiths proves that \frac{d}{dt}\int_{-\infty}^{\infty} |\Psi(x,t)|^2 \, dx = \left.\frac{i \hbar}{2m}\left( \Psi^* \frac{\partial \Psi}{\partial x} - \frac{\partial \Psi^*}{\partial x} \Psi \right)...
  41. E

    Normalization of a wavefunction

    Homework Statement This is a multi-choice question. A particle of unit mass moving in an infinite square well, V = 0 for lxl ≤ a V = ∞ for lxl > a is described by the wavefunction, u(x) = A sin (3∏x/a) If the wavefunction is normalised, What is A? a) 1/2a b) 1/√2a c) 1/√a...
  42. D

    Normalization of radial Laguerre-Gauss

    Homework Statement Normalization of radial Laguerre-Gauss Normalize \Psi _n (r) = h_n L_n (2\pi r^2) e^{-\pi r^2} Homework Equations \int _0 ^{\infty} e^{-x} \, x^k \, L_n ^{(k)} (x) \, L_m ^{(k)} (x) dx = \frac{(n+k)!}{n!} \delta _{m,n} The Attempt at a Solution 1 = \int...
  43. M

    Spherical Harmonics Normalization

    Homework Statement I'm trying to solve I_l = \int^{\pi}_{0} d \theta \sin (\theta) (\sin (\theta))^{2l} Homework Equations the book suggest: I_l = \int^{+1}_{-1} du (1 - u^2)^l The Attempt at a Solution I think it's something related to Legendre polynomials P_l (u) =...
  44. G

    Schrodinger equation normalization to find A -Griffiths

    Homework Statement In David Griffiths Introduction to Quantum Mechanics (2nd ed.), page 32 he normalizes a time independent wave function to get the coefficient A. He dropped the sine part of the integration with no explanation. What is the justification. Homework Equations The time...
  45. J

    Bode plot normalization process

    Hi, I have a 8th order s-domain transfer function that i would like to normalize for plotting a bode plot. The transfer function is in expanded form i.e. s^8 +s^7+s^6 etc. i want to normalise the frequency f by frequency f0 such that s = j(f/f0) instead of just s = j2πf. the reason i...
  46. D

    Normalization of a wavefunction

    Hello, I'm trying to find out the normalization constant in a given wavefunction but I cannot. I think that this is a math problem because I cannot solve the integral of the probability density but your experience could help; I was trying several steps and I tried in the software "derive" but...
  47. P

    Box normalization of plane wave

    Hi everybody. I'm beginning my first course on quantum physics, and our professor introduced the box normalization for plane waves. My question is: why do we need to impose conditions on the borders? I haven't been able to find any explanation on the internet, as every text I found just...
  48. K

    Normalization constant for orbital wave functions

    Suppose I have a wavefunction ψ(r1, r2)= (∅1s(r1) ∅1p(r2) - ∅1s(r2) ∅1p(r1)) And I know that ∅1s(r1) and ∅1p(r1) are normalized. How would I go about finding the normalization constant for ψ(r1, r2)? Everywhere I look just whips out a \frac{1}{\sqrt{2}} out of nowhere...
  49. JK423

    Normalization of a free particle quantum state

    Can anyone explain to me why we use the periodic boundary condition Ψ(x)=Ψ(x+L), in order to normalize the free particle's quantum state?? I've made 2 threads already on this some time ago, but haven't got an answer still.. I hope this time i`ll have because I am really curious about the...
  50. N

    How Does Griffith Prove Psi Stays Normalized in Equation [1.25]?

    I'm having trouble understanding what David Griffith did in equation [1.25]. In this section he's trying to prove that psi stays normalized and I'm following him from [1.21] to [1.25] and where I'm getting stuck is understanding how: ∂/∂t|ψ|^2= i\hbar/2m(ψ*∂²/∂x²[ψ]-∂²/∂x²[ψ*]ψ)...
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