Normalization Definition and 242 Threads

I'm trying to prove that the wave function of Hydrogen for the fundamental state is normalized: $$ \Psi_{1s}(r)=\frac{1}{\sqrt{\pi a^3}}e^{-\frac{r}{a}} $$ What I tried is this: $$ I= \int_{-\infty}^{\infty} | \Psi^2(x) | dx = 1$$ $$ \int_{-\infty}^{\infty} \frac{1}{\pi...

Homework Statement Prove that ##\psi_n## in Eq. 2.85 is properly normalized by substituting generating functions in place of the Hermite polynomials that appear in the normalization integral, then equating the resulting Taylor series that you obtain on the two sides of your equation. As a...

Homework Statement Hi, I am trying to follow my book's hint that to find the normalization factor one should "Diagnoalize ##\Sigma^{-1}## to get ##n## Gaussian which will have variance given by the eigenvalues of ##\Sigma## . Then integrate gives ##\sqrt{2\pi}\Lambda_i##, then use that the...

Homework Statement Obtain the matrix representation of the ladder operators ##J_{\pm}##. Homework Equations Remark that ##J_{\pm} | jm \rangle = N_{\pm}| jm \pm 1 \rangle## The Attempt at a Solution [/B] The textbook states ##|N_{\pm}|^2=\langle jm | J_{\pm}^\dagger J_{\pm} | jm \rangle##...

Homework Statement I don't see how the author normalizes ##u(r)=Asin(kr)##. From Griffiths, Introduction to Quantum Mechanics, 2nd edition, page 141-142: http://imgur.com/a/bo8v6 Homework Equations ##\int_0^{\infty} \int_0^{\pi} \int_0^{2\pi}|A|^2 \sin^2(\frac{n\pi r}{a})r^2 \sin \theta...

I was looking for questions to practice normalizing a wave function, so I visited the following online pdf, http://people.physics.tamu.edu/syeager/teaching/222/hw1solution.pdf. The first question was to find the normalization constant, A of ψ(x) = A cos (2πx/L) for (−L/4) ≤ x ≤ (L/4). After...

Homework Statement For a model of a proton's charge distribution, : [/B] I have to find the constant of normalisation for rho. Homework EquationsThe Attempt at a Solution [/B] I wrote p(r)=p_0 * (e^-r/R)/r I then wrote it as p_0^2 * integral from -infinity to +infinity of (e^-(r/)^2)/r^2 =...

Hi all, I am reading something on wave function in quantum mechanics. I am thinking a situation if we have particles distributed over a periodic potential such that the wave function is periodic as well. For example, it could be a superposition of a series of equal-amplitude plane waves with...

Hello, When we normalize the free particle by putting it in a box with periodic boundary conditions, we avoid the "pathological" nature of the momentum representation that take place in the normal problem of a particle in a box with the usual boundary conditions of Ψ=0 at the two borders. Thus...

Hey everyone, I understand how to normalize a second order system, but I wanted to know if the same steps are taken when the parameters of the system are not scalar but matrices. For example where the parameter phi, and gamma are both 3x3 matrices and X is a 3x1 vector. From what I've see...

Homework Statement So I think I found an error in the solution were it attempts to find q_2^ I'm asked find the orthornomal basis for the column space of matrix A. Homework EquationsThe Attempt at a Solution [/B] My question is in what it puts for q_2^ A_2 = [4/3 4/3 -2/3]^T ||A_2|| =...

I am attempting to normalize a wave function and need to integrate ##\int A^2*e^{(\lambda^2x^2)} dx## going from -inf to +inf. I tried to integrate this on Wolfram Alpha and this was the result. Upon integrating with the parameters the solution is as such. How does the erfi get removed? Do I...

I am trying to clarify what someone means by the words : normalize, reweight. So I'll write what I think they do in practice: 1. Normalization: takes a histogram and scales it by a constant value. The shape of the histogram is not changing, but how the y-axis looks does. 2. Reweight : here I get...

Homework Statement R(ABCDEF) D->F AB->C E->F C->BD D->E Decompose R into dependency preserving 3NF Homework Equations F = {D->F, AB->C, E->F, C->BD, D->E} The Attempt at a Solution My attempt is to first construct the minimal basis for the FD set F, which is G={A->C, E->F, C->B, C->D, D->E}...

I'm reading about stationary states in QM and the following line, when discussing the time-independent, one-dimensional, non-relativist Schrodinger eqn, normalization or the lack thereof, and the Hamiltonian, this is mentioned: "In the spectrum of a Hamiltonian, localized energy eigenstates are...

Hi, i'm performing a simulation about this potential http://motion.cs.umn.edu/PowerLaw/ I calculated the radial distribution function succesfully but i don't know how these guys are normalized the other pair distribution function, as a function of time to collision. Could anyone help me? Thanks!

Hi pf, I am having trouble with understanding some of the steps involved in a mathematical proof that a normalized wavefunction stays normalized as time evolves. I am new to QM and this derivation is in fact from "An introduction to QM" by Griffiths. Here is the proof: I am fine with most of the...

Hi all :I have the table Emp (EmpNum PK, EmpLastNM, EmpEducation, EmpDependent, EmpEducation,...EMpHireDate) which I want to normalize and then I want to do an ERD for it. I must break this into tables one for which , it seems, I cannot have a non-null PK: Now EmpDependent is both...

Homework Statement Show that phi_n will find the proper phi_4. IE: show that it gives the correct normalization constant. Richard Liboff...chapter 7 Homework Equations A_n = (2^n * n! * pi^1/2)^-1/2 The Attempt at a Solution I don't know where to start really. I tried some things with <...

Fermi-Dirac distribution function is given by f(E)=(1)/(Aexp{E/k_{B}T}+1) here A is the normalization constant? How we can get A? E is the energy, k_{B} is the Boltzmann constant and T is the temperature. thank you

Homework Statement An electron in a one-dimensional box with walls at x =(o,a) is in the quantum state psi = A o<x<a/2 psi = -A a/2<x<a A) obtain an expression for the normalization constant, A. B) What is the lowest energy of the electron that will be measured in this state...

Homework Statement I think, to normalize a wavefunction, we integrate over the solid angle ##r^2 dr d\theta d\phi##. Typically we have ## R(r)Y(\theta, \phi) ## as solutions. If ##Y## is properly normalized, then the normalization condition for ##R(r)## ought to be $$ \int_0^\infty dr r^2...

Homework Statement Using the following expression for the Dirac delta function: $$\delta(k-k')=\frac{1}{2\pi} \int_{-\infty}^{\infty}e^{i(k-k')x} \mathrm{d}x$$ Show that if a position space wave function $$\Psi(x,t)$$ is normalized at time t=0, then it is also true that the corresponding...

Hi, if we adopt the convention, a^{\dagger}_\textbf{p} |0\rangle = |\textbf{p}\rangle then we get a normalization that is not Lorentz invariant, i.e. \langle \textbf{p} | \textbf{q} \rangle = (2\pi)^3 \delta^{(3)}(\textbf{p} - \textbf{q}) . How do I explicitly show that this delta...

Homework Statement Consider a free particle, initially with a well defined momentum ##p_0##, whose wave function is well approximated by a plane wave. At ##t=0##, the particle is localized in a region ##-\frac{a}{2}\leq x \leq\frac{a}{2}##, so that its wave function is...

I wonder what the name of this normalization process is for better reference. The scenario is like this: $$\left|\Psi\right> = \frac{1}{\sqrt{6}}\left(\left|a\right>+\left|b\right>+\left|c\right>+\left|d\right>+\left|e\right>+\left|f\right>\right)$$ where each of the components inside the...

Hello Guys, I am trying to Normalize the following wave function but I am getting stuck in between (Maybe maths is the problem here for me). Can anyone please provide some hints. The Wave Function is ψ = e - |x| sin (α x)Please help.

The scalar product of four velocity u with u gives -1. This is said as normalization of four vector. But how does the scalar product yield -1 and what's normalization of four vector. Immediate help required:oldconfused::oldconfused::oldconfused:

Suppose the pdf is A*exp(-mv^2/2kT) , where A is the normalization constant. To obtain A I would integrate the pdf over the all possible values of v. The question is, should the limits be (-infinity,infinity) or [0,infinity) ? It seems that only by choosing the former can I get the correct...

What is the value of ##\left\langle {{\bf{p}}|{\bf{p}}} \right\rangle ## when ##a_{\bf{k}}^ + k\left| 0 \right\rangle = \sqrt {2{E_{\bf{p}}}} \left| 0 \right\rangle ##? (like in Peskin) I suppose that ##\left\langle {\bf{k}} \right|{a_{\bf{k}}}{\bf{P}}a_{\bf{k}}^ + \left| {\bf{k}}...

Hello all, I would like to know how to impose a normalization condition to numerically solving an ODE. For simplicity let's consider the example \frac{dy}{dx}=y You could use different methods using an initial value, but if you consider the interval [x_0,x_1] and \int_{x_0}^{x_1} y(x)dx=1...

Hello, I am very confused how this is true? Where does this come from?? $$<f| \hat{Q}f> = (\sum_{n}a_{n}^{*} |\psi_{n}>)(\sum_{m}a_{m} \hat{Q} | \psi_{m}>)$$ thanks

Homework Statement 2. Homework Equations [/B] Uploaded as a picture as it's pretty hard to type out The Attempt at a Solution So to normalise a wavefunction it has to equal 1 when squared. A is the normalisation factor so we have: A.x2e-x/2a0.x2e-x/2a0 = 1 ∫ψ*ψdx = A2∫x4e-axdx = 1 Then I've...

Homework Statement Well it is not the problem itself that bothers me but the maths behind a part of it. As part of finding the coefficient I had to solve the integral of (Sin(x))^(2l+ 1). The solution given by the solution manual just pretty much jumps to the final answer...

when considering the quantum harmonic oscillator, you get that the wave function takes the form psi=ae^{-\frac{m\omega}{2\hbar}x^2} I have been trying to integrate \psi ^2 to find the constant a so that the wave function is normalised, and I know the trick with converting to polar coordinates...

Hello everyone: I didn't have a complete view of the quantum field theory and cannot understand this question. We now there will always be fluctuation field in the universe which corresponds to the ground state energy 1/2hw of harmonic oscillator. In the free space, we will use box...

Hey all, This question may sound daft, but how do I normalize angular frequency? For a little background: I'm trying to optimize some circuits, and I've managed to write some successful code using the "Design of Ultra Wideband Antenna Matching Networks" book, but the code requires normalized...

Homework Statement A particle is described by the wave function psi(x) = b(a2-x2) for -a < x < +a and psi(x) = 0 for x < -a and x > +a, where a and b are positive real number constants. a) Using the normalization condition, find b in terms of a. b) What is the probability to find the particle...

In Griffith quantum mechanics, it is written that for a wavefunction to be normalizable, it is essential that the wavefunction approaches zero before 1/ √(|x|) as x tends to infinity... Please explain from where this condition has been derived.

Homework Statement Using the normalization condition, find the constants λ and a of: f(t)=ae^(-λt) Homework Equations integrate from t=-∞ to t=∞ of the function and set it equal to one The Attempt at a Solution I used to be good at these but something is slipping my...

Homework Statement These are rather simple questions but the rules for all of this are not quite clear to me yet. I'm to determine whether or not the following states are "legal" and if not I should normalize them. a. ##\frac{1}{√385} ∑_{x=1}^{10}x^2 |x>## b. ##\frac{1}{√2}...

The wave function solution psi is a function of time and position. Hence the integral of its square over all x will, in general, give a function of time. To normalize this, we must multiply with the inverse of the function. Therefore it seems that the normalization constant does not remain...

Hi I have been working my way through some past papers and then checking the solutions but I am confused about the following. One question asked for the normalisation constant for the following wavefunction ψ( r, θ , ø ) = Aexp(-r/R) where R is a constant. The solution requires a triple volume...

I'm working with some old software to optimize antenna networks, and I've come across some stuff that I don't understand. For the software to run, all impedence values entered must be normalized to 1 ohm. What does it mean to normalize an impedence and how do I do it? Also, the manual for the...

On page 13 of Griffith's "Introduction to Quantum Mechanics 2nd ed" David goes into a long (relatively speaking) proof of why a normalized pair of quantum state vectors will not at some time later become "un-normalized". It seems like just putting the Psi's in a braket the e^(-it) "time...

Homework Statement Consider the wave function $$\Psi(x,t)=Ae^{-\lambda|x|}e^{-i\omega t}$$ Where ##A##, ##\lambda##, and ##\omega## are positive real constants. (a)Normalize ##\Psi##. (b)Determine expectation values of ##x## and ##x^2##. Homework Equations...

In Srednicki's QFT textbook, equation 9.6, he writes: Z[J]=e^{i \int d^4x \, \mathcal L_I\left(\frac{1}{i}\frac{\delta}{\delta J(x)} \right)} \int \, \mathcal D\phi e^{i \int d^4x \, \mathcal [\mathcal L_0+J\phi]} \propto e^{i \int d^4x \, \mathcal L_I\left(\frac{1}{i}\frac{\delta}{\delta...

I have these questions on the exam after three days I do not know how to solve Please help me http://im57.gulfup.com/qzZrpe.jpg http://im57.gulfup.com/7lwZaV.jpg http://im57.gulfup.com/FCHM55.jpg

I do understand the probability of a wave function ψ is given by ∫ψ* ψ d3x, which after normalization is equal to 1. However, I then saw the following, ∫ψn* ψm=δmn Here is my understanding, the discussion is about discrete eigenfunction and value as expressed in m and n, ψn and ψm are two...

I'm trying to understand what is the correct rule for the Dirac delta normalization of a non-integrable wave function, and can't seem to find any decent references. My issue is with achieving the proper dimensionality of the resulting wave function. This would be length-1/2 for the states of a...