Normalization Definition and 229 Threads

[SOLVED] Normalization of wave functions Mainly my question is that with the normalization of a wave function in quantum mechanics we use \int_\infty^\infty |\Psi(x,t)|^2 dx = 1 and we can solve for a constant we may have been given in the problem. Homework Statement Determine...

[SOLVED] Particle in a box Homework Statement A particle is described by the wave function \Psi(x)=Ae^{(-bx^2)}. Calculate the normalization factor A. Homework Equations & The Attempt at a Solution So, to normalize \psi(x), we integrate the probability (\Psi(x)^2) over the entire area (this...

Homework Statement I'm trying to determine a normalization value, A, for the following wavefunction: \Psi = Ax{^2}exp(-\alpha x)}, x>0 \Psi = 0, x<0 In the past, I've had an i term in my exponential, so when applying the Normalization Condition: \int|\Psi(x)|^2 dx = \int\Psi{^*}(x)...

a.) Apply Normalization condition for the n=3 Ѱ-solution to find constant B. b.) Find <x> c.) Find <p> d.) Calculate probability that particle of mass m is located between 0 and a/2. Given: Ѱn(subscript)(x) = Bcos(n*pi/a)x Solution to ∞ square well from -a/2 to a/2 (Width "a"...

Hello, How do I find the normalization constant for psi(x,y,z) = N exp -(x/2+y/2+z/2) ?? I did the following: \int(psi^* psi)dx dy dz = 1 the integral bounds are from -infinity to infinity and the * means the complex conjugate.The integral is so weird that I couldn't find N. I used...

I need to normalize the following wave function: psi= Cexp(-abs(x))exp(-iwt)cos(pix) I know that when squaring it, the time dependent part drops out, which is good, but what I seem to be left with is Psi^2=C^2exp(-2abs(x))cos^2(pix) Which seems like a fairly complicated integral to...

Ok, I'm trying to recreate some results from a paper, and I am really lacking in understanding. I'm getting extremely frustrated. I'll try to create a similar problem that replicates the original problem. The original problem, is three coupled non-linear differential equations that must be...

Homework Statement A quantum system has a measurable property represented by the observable S with possible eigenvalues nh, where n = -2, -1, 0, 1, 2. The corresponding eigenstates have normalized wavefunctions \psi_{n}. The system is prepared in the normalized superposition state given by...

Homework Statement Given that the antisymmetric spin function for a 2 electron system is N[a1b2-a2b1], find the normalization constant N. (and by a and b I mean the alpha and beta spin states and by 1 and 2, I mean the labels on the two electrons... Homework Equations Normalization...

A wave function (psi) equals A(exp(ix)+exp(-ix) in the region -pi<x<pi and zero elsewhere. Normalize the wave function and find the probability of the particle being between x=0 and pi/8 Equation is : the integral of psi*(x,t)psi(x,t)=1 for normalization

Homework Statement I understand how you normalize vectors to unity, but how would you normalize a function to unity? For example, how would you show that the function (2/L)^(1/2) sin(n*pi*x/L) is normalized to unity? You cannot just just take its modulus and set it to one since because x...

Homework Statement Show that the (1,0,0) and (2,0,0) wave functions listed in table 7.1 are properly normalized. http://www.geocities.com/greenlran/phtable712.jpg Homework Equations psi.n.l.ml.(r,theta,phi)=R.n.l.(r)THETA.l.ml.(theta)PHI.ml.(phi) The Attempt at a Solution To...

Homework Statement The wave function of a particle is Y(x,t) = A e^-kx*e^-iwt for x greater than or equal too 0, and it is zero everywhere else. What is the numerical value of the normalization constant A for k=5.55 1/nm and w =7.19 1/ps? Homework Equations intergral Y^2=1 The...

1.Question. the unnormalized excited state wavefuction of the H atom is: \psi = ( 2 - r/a_0 ) e^a where a = -r/a_0 Normalize the function to one. 2. My attempts. I tried 'integrating' the psi*psi, i.e. I squared the above wavefuction. N^2\int_{0}^{\infty} R^2e^{2a}\int_{0}^{\pi}sin...

I was given this wavefunction and asked to find the normalization factor, N. lpsi>= N[2 lphi1> - lphi2> +i lphi3>] I am confused as to how to get this problem going. Do I just take <psi l psi> and set it equal to one? I probably have many more questions to ask, but...

This may be a simple problem, but I wanted to run it by some other people before using my solution. I have two distinct sets of items A and B which may or may not be connected to one another. I want to know whether or not the interconnections between them are significiantly different, i.e are...

Hi all! I hope somebody is able to help me on my way with this question. I have been asked to show that the Normalization factor for the 1s atomic orbital of H is 1/(\Pi a_o^3)^\frac{1}{2}. The wavefunction is \psi(r) = N exp(-r / a_o) I'm given dt = r^2 sin \Theta and dr d\Theta d\Phi and...

Hi all! I hope somebody is able to help me on my way with this question. I have been asked to show that the Normalization factor for the 1s atomic orbital of H is 1/(\Pi a_o^3)^\frac{1}{2}. The wavefunction is \psi(r) = N exp(-r / a_o) I'm given dt = r^2 sin \Theta and dr d\Theta d\Phi and...

Hi there I'm stuck on one of the normalization question, I'd be glad if you can help me out. The questions is, psi(r)=Ne^(-ar) where N is a normalization constant and a is a known real parameter. Solution reads, 1=int dr lpsi(r)l^2 = 4piN^2 int (from 0 to infinity) dr r^2 e^(-2ar) What I...

Help, I'm losing it :cry:. Wavefunction of Hydrogen atom in the ground state is: \Psi (r) = Ae^{-r/r_0} Determine A. I set about trying to obtain the Normalization factor. \int \Psi^2 (r) dV = 1 \int \left(A^2 e^{-2r/r_0}\right)(4\pi r^2)dr = 1 What limits should I take for this integral?

For this given wavefunction of a hydrogen atom in 2s state, verify if the function is normalized: \psi_{200} = \frac{1}{\sqrt{32\pi a^3}}\left(2 - \frac{r}{a}\right)e^{\frac{-r}{2a}} My work: I have to verify: \int_{all space} \psi_{200}^2 dV = 1 dV = 4\pi r^2dr So, \int_{all space}...

Normalization of a wavefunction Let Phi be a wave function, Phi(x)= Integral of {exp(ikx) dk} going k from k1 to k2 I'm having trouble normalizing the wave function. I calculated the integral, then multiply by its conjugate and now I'm supposed to integrate again /Phi(x)/^2 in all...

I have been trying to figure out how to find the normalization constant for the ground state harmonic oscillator wave function. So: \int_{-\infty}^{\infty} {\psi_0}^2 (x) = 1 {\psi_0}^2 (x) = A^2 e^{-2ax^2} \int_{-\infty}^{\infty}A^2 e^{-2ax^2} = 1 A^2...

Why needing normalization technique?? Why do we have to normalize an experiment for instance in microarray or transfection? Thanks.

How do I calculate the normalization constant for a wavefunction of the form (r/a)e^(-r/2a) sin(theta)e^(i*phi)? How would I write the explict harmonic oscillator wavefunction for quantum number 8(in terms on pi, alpha, and y) thanx

There is this excersise in Griffith's QM text that I can't seem to solve. It's about the calculation of the normalization factor of the spherical harmonic functions using the angular momentum step up operator. These definitions/results are given: Y_l^m = B_l^m e^{im\phi} P_l^m (\cos\theta...

I am familiar with the normalization \int\left|\Psi\right|^{2}dx=1 Because we want to normalize the probability to 1. However if a state vector isn't in the x basis and is just a general vector in Hilbert space, we can take the normalization condition to be: <\Psi|\Psi>=1...

How do I find the value of the normalization constant A for the wave function Ψ = Axe ^ (-x squared/2)? I know that I set it equal to 1, but do i do the integral from negative infinity to positive infinity; for no other limits are given?

I realize that when we normalize a solution to the Schrodinger equation, that we are setting it equal to 1, in order to maximize our chances of finding it. The question which I have is how do you normalize : lψl^2 = Axe^((-x^2)/2). The problem which I see is the e^(-x^2)/2). What would you...