Normalisation Definition and 52 Threads

Hi everyone, I'm really new to MCNP here and I'm "playing" around trying to understand what is going on. I'd like to plot my tallies (F2, F4 and F6). Is there any tool (e.g. python or matlab package) you recommend? I know that the internal plot MCPLOT is available but I'm wondering how you...

Normalize function f(r) = Nexp{-alpha*r} Where alpha is positive const and r is a vector I was just wondering if the fact that we have a vector value in our equation changes anything about the solution

I can't figure out how they get i/sqrt(2) for normalisation of c1. Why is it a complex number? If I normalise c1 I just get 1/sqrt(2) because i disappears in the absolute value squared. Thanks

Hi, I just have a quick question when I was working through a linear algebra homework problem. We are given a matrix A = \begin{pmatrix} 2 & -2 \\ 1 & -1 \end{pmatrix} and are asked to compute e^{A} . In earlier parts of the question, we prove the identities A = V \Lambda V^{-1} and e^{A}...

The previous part was to show that ##a_+ \psi_n = i\sqrt{(n+1)\hbar \omega} \psi_{n+1}##, which I just did by looking at$$\int |a_+ \psi_n|^2 dx = \int \psi_n^* (a_{-} a_+ \psi_n) dx = E+\frac{1}{2}\hbar \omega = \hbar \omega(n+1)$$so the constant of proportionality between ##a_+ \psi_n## and...

My problem is in (b) it written sketch psi (X,0) as function of X , why the answer was like this I didn't understand the branch from a to b Best

In my lecture notes, the normalisation for such a bosonic state was given by However, I can't quite seem to grasp how the normalisation factor came about. Could someone walk me through it? Many thanks in advance!

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...

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...

Okay, so I've been set this homework to find the normalisation constant, N, for the radial wave function in the 2s state for hydrogen (my title was too long to fit that vital information in). thing is; I'm having a bloody hard time and in the process confusing myself with trying to take out all...

Hi, I'm reading about the wave packet solution to the dirac equation but in the book I'm reading it states that \int \frac {d^3p} {(2\pi)^3 2E} [a u e^{-ipx} + b^\dagger \bar{v} e^{ipx} The normalisation constant confuses me. I guess the 2pi^3 is reasonalbe. However, the 1/2E seems a bit...

Homework Statement Find relation between real normalisation constants ##B_1## and ##B_2## for the following wavefunction, $$ \Psi_k =\sum_{k=1,2} \frac{B_k}{\sqrt{4\sigma ^2 + 2it}} \exp (ip_k (x - \frac{p_k}{2}t) - \frac{(x - p_k t)^2}{4\sigma ^2 + 2it}) $$ The working is rather long so...

Homework Statement Consider the wavefunction: Ψ(x, t) = Ae-λ|x|e−iωt Normalise Ψ(x, t) Homework Equations ∫ |Ψ(x, t)|2 dx = 1 (bounds from x: -∞ to +∞) The Attempt at a Solution Ψ(x, t) = Ae-λ|x|e−iωt Ψ(x, t) = Ae-λ|x|−iωt Ψ*(x, t) = Ae-λ|x|+iωt ∫ |Ψ(x, t)|2 dx = A2 ∫...

Hi there - just a quick question about Fourier transforms: When learning about quantum mechanics, I found that the Fourier transform and inverse Fourier transform were both defined with constants of ##{ \left( 2\pi \right) }^{ -d/2 }## in front of the integral. This is useful, as...

Homework Statement See Image, Sorry Its easier for me to attach images than writing all equation on the forum's keyboard! I only need to check if I'm working it out correctly up to the position expectation value because I don't want to dive in the rest on wrong basis ! Homework Equations...

According to my textbook the nonlinear Schrödinger equation: $$\frac{\partial A(z,T)}{\partial z} = -i \frac{\beta_2}{2} \frac{\partial^2A}{\partial T^2} + i \gamma |A|^2 A \ \ (1)$$ can be cast in the form $$\frac{\partial U(z,\tau)}{\partial z} = -i \frac{sign \beta_2}{2} \frac{1}{L_D}...

The triplet spin state with a normalisation constant of 1/√2 and the singlet spin state with the same normalisation constant... Where on Earth is this normalisation constant derived from? I've been scouring the Griffiths intro to quantum mechanics textbook and can't find info on it.

Homework Statement The Hamiltonian for an atom of deuteron is ##\hat{H} = \frac{-\hbar^2 \nabla_R^2}{2M} - \frac{\hbar^2 \nabla^2}{2\mu} - Ae^{\frac{-r}{a}}## Where ##\nabla_R## is the differential operator for the centre of mass co-ordinates ##R = \frac{m_p\vec{r_p} + m_n\vec{r_n}}{M}## and...

Homework Statement Verify that a plane wave ψ(x) = Ae-ikx is a solution to the time independent Schrodinger equation for a free particle in one dimension. Can it be normalised? Why?[/B]Homework EquationsThe Attempt at a Solution My lecturer's notes are all over the place, which is frustrating...

1. The problem: Building a (probably very simple) computational model for Ising Spins - particles on a lattice with spin up and spin down, only nearest neighbour interactions. I can't for the life of me figure out the renormalisation constant for the probability of a given particle flipping...

The wavefunction ##\Psi(x,t)## for a free particle is given by ##\Psi(x,t) = A e^{i(kx-\frac{\hbar k}{2m}t)}## This wavefunction is non-normalisable. Does this mean that free particles do not exist in nature?

Hey there, I used Mathematica to find the (non-normalised) wave function of an electron in the vicinity of a Hydrogen nucleus, and converted the answer from one involving Whittaker functions to one involving generalised Laguerre polynomials. My result is shown below: This agrees with the...

Homework Statement Given a wave function psi, \psi (x) = A \sqrt{|x|} e^{- \beta x^2} where \beta is a constant (take the positive square root) . Normalise the wave function and hence find A. Homework Equations ? The Attempt at a Solution This is my first attempt at a problem like this, and...

Hi all, I am currently operating a piece of equipment that essentially collects particles and separates them based on their size. Essentially you have 8 stages, and each stage has a differing size of particles it collects. For example: Stage----Size of Particles (D) (um)-----Mass Collected (M)...

Homework Statement Consider the wavefunction ##\Psi (x, t) = c\ \psi (x) e^{-iEt/ \hbar}## such that ##\int | \Psi (x, t) |^{2} dx = 1##. I would like to prove to myself that the normalisation factor ##c## is a real number. Homework Equations The Attempt at a Solution ##\int | \Psi (x, t)...

Homework Statement The transition amplitude for the harmonic oscillator may be written as ##\langle x_2, t_2 | x_1, t_1 \rangle = N_{\omega}(T) \exp(i/\hbar S_{cl})##, where ##T=t_2-t_1## and ##S_{cl}## is the classical action. Let the wave function at ##t=0## be ##\psi(x,o) =...

Homework Statement Calculate the normalization parameter A in the wavefunction ## \varPsi(x,t) = A e^{i(k\chi - \omega t)} ## for a beam of free protons traveling in the +x direction with kinetic energy 5 keV and a density of ##7.5 * 10^9 ## particles per meter beam length. Homework...

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 Following gaussian wave packet: ## \psi (x)= \frac{1}{\sqrt{\sqrt{\pi a^2}}} e^{-\frac{x^2}{2a^2}}## Prove that this function is normalized. Homework Equations ## \int_{- \infty}^{\infty} |\psi (x)|^2 dx = 1## The Attempt at a Solution Is ## \frac{1}{\sqrt{\sqrt{\pi a^2}}}...

Homework Statement The questions are in the file. Hint: Part (a) asks you to find the normalization constant for P(N, R). Note that this is a 3D distribution: P(N, R)dRxdRydRz gives you the probability of finding R in a certain "differential volume" of size dRxdRydRz located at the vector...

Homework Statement Determine the constant λ in the wave equation \Psi(x) = C(2a^2 x^2 + \lambda)e^{-(a^2 x^2/2)} where a=\sqrt{mω/\hbar} Homework Equations Some standard integrals I guess The Attempt at a Solution So I believe the wave equation just needs to be normalised...

In our physics class of quantum mechanics, we constantly talk about normalisation and normalising wavefunctions such that the total probability of finding the particle in infinite space is one. I don't get why do we normalise and how do we normalise(I have not taken up statistics course). It...

Hi, Just a little thing that's been puzzling me: Consider a state \mid \psi \rangle = \frac{1}{\sqrt{2}} \mid A \rangle + \frac{1}{\sqrt{2}} \mid B \rangle This is normalised since [\frac{1}{\sqrt{2}}]^2 + [\frac{1}{\sqrt{2}}]^2 = 1 Now let A = B: \mid \psi \rangle =...

Hello all! I'm trying to understand the standard normalisation of the scale factor to be set to 1 at today's time. Looking at the first Friedmann Equation for a spatially flat Robertson Walker metric with no cosmological constant gives \frac{\dot{a}^2}{a^2} = \frac{8\pi G}{3}\rho If we...

Homework Statement Consider the wave packet \psi(x)\equiv ψ(x, t = 0) = Ce^{i\omega x}e^{-\left|x\right|/2\Delta x} where C is a normalisation constant. Normalise \psi(x) to unity. Homework Equations The Attempt at a Solution I know the normalisation condition. My problem is when...

Just a quick question, I'm looking to express the normalisation condition formally mathematically, is this acceptable: 1=\int_R|\psi|^2 \ \mathrm{d}\tau For a particle in 3 dimensional region R.

Just a quick question--long story short, I need to normalise a plot by the cross-section, but I'm not sure how to do that and the Google hasn't been too helpful. I was thinking about scaling it by the cross-section times the luminosity--does this sound reasonable?

What condition must a 1D wavefuntion satisfy to be normalised? Is the fact that it the wavefuntion squared has to equal the probability of finding a particle or that the wavefuntion has to be finite or something totally different?? please help, thanks

Homework Statement find the normalisation constant (A) Homework Equations wave functcion \psi (x,t)= A[3sin(\frac{\pi x}{L})+2sin(\frac{2\pi x}{L}] The Attempt at a Solution A^2\int_{0}^{L}[\psi(x,t)]^2dx=1 A^2\int_{0}^{L}[9sin^2(\frac{\pi x}{L})+12sin(\frac{\pi...

Homework Statement i. Confirming the wavefunction is normalised ii. Calculating the expectation values: <\hat{x}> , <\hat{x^{2}}> , <\hat{p}> , <\hat{p^{2}}> as a function of \sigma iii. Interpreting the results in regards to Heisenberg's uncertainty relation. Homework Equations...

Homework Statement a particle of mass m, confined to a one dimensional infinite potential of 0\leqx\leq1 V(x) = 0 elsewhere V(x) = \infty Homework Equations Choose as a trial wavefunction \Psi(x) = Nx[1 - \alphax + (\alpha - 1)x^{2}] Verify that N^{2} = \frac{K}{16 -...

Homework Statement Normalise the wavefunction: \Psi(x) = C exp(-mwx^{2}/(2h)) for the 1-D harmonic oscillator. Homework Equations \int\Psi*\Psidx = 1 The Attempt at a Solution I used the following integral from -inf to inf: ¦C¦^2\intexp(-ax^2)dx = srqt(pi/a) where a = const...

Hey guys, Homework Statement I have an assignment, which is to Solve Schrodinger's equations, for a certain potential distribution, which can be divided up into three regions. A solution for one of the regions is of the form: Ae^{kx} If you substitute this into Schrodinger's...

Hi, 2nd year physics student here doing a past paper on quantum mechanics everything is going nice and dandy then this happens.. question: prove that the normalisation constant A is given by A = \frac{1}{2^1^/^2} (\frac{a}{\pi})^1/4 ok seems fairly straight forward but i keep getting...

Homework Statement Suppose you assume that you have normalised a wave function at t = 0. How do you know that it will stay normalised as time goes on? Show explicitly that the Schrodinger equation has the property that it preserves normalistion over time. Homework Equations From my notes I...

Homework Statement Question: Given that Wavefunction Fi = A exp[b*mod(x)], which b is a non zero positive constant. Calculate the normalisation constant. Homework Equations 1 = Integrating Mod square (Wavefunction) from minus infinity to positive infinity The Attempt at a Solution...

I'm looking right now at what purports to be the normalisation condition for the associated Laguerre polynomials: \int_0^\infty e^{-x}x^k L_n^k(x)L_m^k(x)dx=\frac{(n+k)!}{n!}\delta_{mn} However, in the context of Schroedinger's equation in spherical coordinates, I find that my...

Normalisation constant~ help~~ Homework Statement An electron is in the spin state |> = A (3i, 4), so determine the normalisation constant A. Homework Equations :rolleyes: :frown: The Attempt at a Solution :cry: Well, I get confused about this questions, can anybody tell me what...

Homework Statement A hydrogen atom in the ground state can be described by the following wavefunction: \Psi(r) = \frac{C}{\sqrt{4\pi}}e^{- \frac{r}{a_{0}}} Normalise this wavefunction. The Attempt at a Solution I did this and got: C = \sqrt{\frac{8\pi}{a_{0}}} I have no way of checking...

Are normalisation constants in physics always real valued? If yes, is that because the normalisation constanst only normalises measureable quantities which are always real so the constants are real also. Any exceptions?