Normalization Definition and 229 Threads

I'm given a wavefunction (I think it's implied this is some sort of solution to the Schrodinger equation) in my quantum mechanics class, and I need to normalize it to find its constant coefficient. So I have $$\psi(x)=Ne^{-\frac{|x-x_o|}{2a}}$$ And the formula for normalizing this to find \(N\)...

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=...

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...

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...

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...

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...

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.

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...

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...

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...

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...

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...

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 :(

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...

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)...

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...

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...

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...

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...

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...

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}...

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...

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...

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) =...

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...

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...

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

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...

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...

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...

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})...

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, & \;\...

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...

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...

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...

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...

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)...

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...

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...

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) =...

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...

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...

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...

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...

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...

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...

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)...

Homework Statement how to set up integrals for normalization of sin(\theta)e^(-i\phi) Homework Equations The Attempt at a Solution

I have a 40*40 matrix which has elements very close to 1 on diagonal and very small off-diagonal elements. I find determinant of many of these randomly generated matrix, determinant is roughly multiplication of diagonal matrix squared. As (.95)^40 is a small number and (1.05)^40 is a bignumber...

Homework Statement Determine the normalization constant c in the wave function given by \psi(x) = c cos(kx) exp[(-1/2)(x/L)2 ] Homework Equations 1=\int |\psi(x)|2 dx limits of integration being -inf to inf. The Attempt at a Solution I'm very much sure that my math is wrong...