Normalization Definition and 229 Threads

(Note: although arising in QM, this is essentially a calculus question) Ѱ (x) = A sin (n╥x/a) 1 = ∫ l Ѱ (x) l^2 dx with limits of integration a to 0 1 = ∫ A^2 sin^2 (n╥x/a) dx with limits of integration a to 0 Indefinite integral ∫ sin^2 x dx = x/2 - sin2x/4 I know this integral...

Hello! Homework Statement I'm revising my quantum mechanics course, but I don't get this normalizing-problem. \psi = N r cos \theta e^{-r/a_0} To begin with, this is how my teacher solves it in the solutions manual: 1=N^2\int_0^\infty r^2 e^{-r/a_0} r^2 dr \int_0^{\pi} \int_0^{2 \pi}...

Hi! I have a little question which is puzzling me. Maybe it is a very simple question. It is my understanding that the Fermi-Dirac distribution is a probability density function and, as such, its integral between 0 and infinite should be 1. When T = 0, the integral gives the chemical...

I just want to ask this: what is the physical meaning of wavefunction's normalization? thanks for everyone in advance

Homework Statement A particle is in an angular momentum state Ψ(θ,φ) = |l=1,m=1> + 2|1,0> + 3|1,-1> Normalize this state and find the probabilities for finding the system with its third component Lz with values hbar, 0, -hbar. Homework Equations The Attempt at a Solution...

Homework Statement psi(x) = A(1 - e^(ikx)) if 0 < x < 2pi/k Homework Equations integral of psi * psi conjugate over all space = 1 The Attempt at a Solution the conjugate is psi*(x) = A(1 - e^(-ikx)) so when I multiply psi and psi* , I get 2 - e^(-ikx) - e^(ikx) I can't...

How to obtain the coefficients of normalized wavefunction for the hybrid orbital in sp2 hybridization (esp in BH3) , which normally in surds? In what way symmetry affect the linear combination of the atomic orbitals ? Will appreciate if anyone could help or provide some beginning guides , thanks...

Question: 1. An electron is freely moving in a one‐dimensional coordinate, x . At some point t in time, its (complex‐valued) wavefunction is ψ (x,t) = Ceiωte−(x / a)2 . a. Why must \int \left|\Psi|2=1? b. From the so‐called normalization requirement given in part a., determine the...

I have two wavefunctions that I need to normalize but I cannot figure out how to get them into an acceptable integrable form... the first is psi=(2-(r/asub0))*e^(-r/asub0) the second is psi=rsin(theta)*cos(phi)*e^(-r/2asub0) I know these need to be in the form (where psi will be name y for...

Homework Statement I am following a derivation of Legendre Polynomials normalization constant. Homework Equations I_l = \int_{-1}^{1}(1-x^2)^l dx = \int_{-1}^{1}(1-x^2)(1-x^2)^{l-1}dx = I_{l-1} - \int_{-1}^{1}x^2(1-x^2)^{l-1}dx The author then gives that we get the following...

I've two electromagnetic waves (light) with amplitudes 1x (normal) and 2x (double) amplitude. And I want to pass these two waves through a "normalizer" expecting 1x amplitude for both waves. Question is: Is such a "normalizer" possible and/or exists. I'm not looking for any electronic...

Homework Statement \psi=B( sin px/L + sin 2px/L ) Homework Equations lineer combination of two waves n=1 and n=2 states particle in a box wide L The Attempt at a Solution I have no idea how to calculate lineer combination of two waves normalization. How do I get B normalization...

1. Find the normalization constant for the radial wave function for Hydrogen. I'm told that C = 1/(24a^5)^1/2 But how do I get that? 2. n=2, l=1 R(2)(1)=Cr^(-r/2a。) the integral from 0 to infinity of (x^4 * e^-"alpha"x) = 24 / alpha^5 3. I honestly don't know where to start

Homework Statement I am given a trial function and before I use the variational method, I need to normalize the trial function. This is easy usually, but I don't know what to do in this specific case: The trial function is: X[x]=N1(1-x^2)+N2(x-x^3) Domain: -1<x<1 N1 and N2 are the...

For a continuous eigen-basis the basis vectors are not normalizable to unity length. They can be normalized only upto a delta function. At the same time for discrete eigen basis the basis vectors are normalizable to unity length. What about the systems with both discrete as well as continuous...

Homework Statement To test my knowledge of Sakurai, I asked myself to: "Prove that an operator being unitary is independent of basis." The Attempt at a Solution I want to show the expansion coefficients’ squared magnitudes sum to unity at time “t”, given that they do at time t = t0...

I am pretty sure that I'm doing this right but the integral for normalization seems impossible. Here is the question: Normalize this wave function. psi(x,t)=Axe^(-sqrt(km)/2h)*x^2))*e^(-i(3/2)(sqrt(k/m)*t) for -infinity<x<+infinity where k and A are constants and m is given. I used...

why it is not possible to normalize the free-particle wawe functions over the whole range of motion of the particles?

I want to know how to normalize symmetric and anti-symmetric wave functions ??

So, I'm taking an EE class and my teacher is terribly handwavy. She couldn't really explain this to me (not homework, lecture). I detect a fundamental problem in the math, coming from a science background, but it could just be my ignorance: Here's her lecture: physical setup: a...

Homework Statement Show that the (1 0 0) and (2 0 0) wave functions of hydrogen atom are properly normalized. Homework Equations I know that (n l ml): (100) = (2/a^(3/2)) exp^ (-r/a) (200) = (1/((2a)^(3/2))*(2-r/a) exp^(-r/2a) The Attempt at a Solution I started with...

hello i attached my question if i can get some help i think that there is another way to solve this problem

I know that in Minkowsky space, the 4-velocity is normalize according to the following relation: \eta_{\mu\nu} U^{\mu} U^{\nu} = -1 Can someone explain to me ho this can be generalized to a normalization in a curved space with the following relation : g_{\mu\nu} U^{\mu} U^{\nu} = -1...

Homework Statement A hydrogen atom given the following state: \psi (r, 0) = A\psi_{100}(r) + (\frac{1}{\sqrt{5}})\psi_{311}(r) + (\frac{1}{\sqrt{3}})\psi_{422}(r) I must normalize this to solve for the normalization constant A Homework Equations The Attempt at a Solution Is it just me or...

In Peskin's textbook, he uses the spin sum as \sum u\bar{u} = \gamma^{\mu}p_{\mu} +m ; on the other hand, in Kaku's book and in Zee's book, they use \sum u\bar{u} = \dfrac{\gamma^{\mu} p_{\mu} + m}{2m} . But why aren't there any diffferent in the differential cross section formula ?

I'm looking at a guide by Texas Instruments on active filter design. In it are the following equations for a second order lowpass filter, verbatim: The coefficient form of the denominator: s^2 + a_1s + a_0 Normalized: P(s) = (\frac{s}{\sqrt{a_0}*\omega_c})^2 + \frac{a_1s}{a_0*\omega_c} + 1...

Hi all, I am about to begin my studies as an experimentalist and I keep hearing about these terms when someone represents his data as histograms. Can some one here, please, give me a clear explanation about their meanings. My background is theory and you can use as much mathematics as you...

Hi, i need some help regarding normalization of a wave function, i feel it is a very simple problem, but i am having a hard time figuring it out. I would really appreciate it if anybody could help me out a bit regarding this. I need to normalize the following wavefunctions by figuring out the...

Homework Statement Normalize sin ((n*pi*x)/L) where x is between 0 and L and n is a positive integer Homework Equations integral (psi*psi)dx=1 N^2 integral sin ((n*pi*x)/L)dx =1 I don't really understand if this integral is correct, what is the complex conjugate of the wavefunction...

I need to show that the spherical harmonic, Y^-1 of l=1 is Normalized. Y(m=-1, l=1) = sqrt(3/(8(pi))sin(theta)exp(-i(thi))

I was in my Electrodynamics lecture last week, still working the Laplacian and Poisson equations, when we discussed an infinite parallelpipid (infinite in the x direction, length a and b in the y and z direction respectively) with a potential of \Phi=\Phi_0 at x=0 plane and every other face...

Hey folks. I was asked to confirm that the attached discrete function is normalized. The function to check the normalization that I was provided with is \frac{1}{2}\sum^{N}_{i = 1}P_{i}(\Theta)\Delta\Theta_{i} = 1 No matter what I do, I get a number on the order of 10^4, not...

What does NORMALIZATION do?I am using a mathematical tool in which tables are formed and normalization of these tables are done using formula u know: g(x)=g(x)/Max[g(x)]; i.e all values of the table are divided by the Maximum number from the table. thus table got maximum value =1. my...

Hi, In Lewis Ryder's QFT book on page 160, the propagator for the case when the Lagrangian can be written as L = \frac{p^2}{2m} + V(q) is given as \langle q_f t_f|q_i t_i \rangle = \lim_{n\rightarrow\infty}\left(\frac{m}{i\hbar\tau}\right)^{(n+1)/2}\int...

Hello, everyone! I'm working on parametrizing a magnetic field using spherical harmonics. The equations Yc n,m (theta, phi) = (R/R0)^n * Pn,m(cos(theta)) * cos(m*phi) Ys n,m (theta, phi) = (R/R0)^n * Pn,m(cos(theta)) * sin(m*phi) where Pn,m is a Legendre polynomial where n is degree and m...

Homework Statement normalize the wave function \Psi(x)= Acos(\Pi*x/a) to show that A=\sqrt{2/a} The Attempt at a Solution i don't know how to get that answer as all i can tell, normalizing gives: -A^{2}pi^{2}2x/a^{2} * sin (pix/a) However this does not give the right answer for A Any...

Homework Statement (1) For the cubic 3D infinite-well wave function, \psi(x,y,z) = A sin(n\pix/L)sin(n\piy/L)sin(n\piz/L) Show that the correct normalization constant is A = (2/L)^{3/2} Homework Equations Note: The Pi's above are not meant to be superscript, and each n relates to...

In attempting to work through some basics of QM – I have a question regarding a statement or a conclusion regarding “Normalizing the Wave Function” After “turning the crank” authors show: \frac {d}{dt} \int_ {-\infty}^{\infty}|\psi|^2 dx= \frac{ih}{2m}(\psi*\frac{d\psi}{dx} -...

Homework Statement I'm starting to (trying) teach myself some quantum mechanics out of the Griffiths book, and since there are no answers in the back I have no idea if I'm on the right track or not. Could you guys look over the answer to this equation to see if it looks right? Consider the...

Homework Statement Trying to normalize the first excited state. I have, 1 = |A_1|^2(i\omega\sqrt{2m}) \int_{-\inf}^{\inf} x \exp(-m\omega x^2/2\hbar) How do I do the integral so I don't get zero since it's an odd funciton?

Question Free particle in 1D where V(x) = 0. There is a general boundary condition \psi(x+L)=e^{i\theta}\psi(x) used for box normalization which has arbitrary phase theta. E=k^2\hbar/(2m) is true for free particle energies. Attempt Comparing with the condition \psi(x+L)=\psi(x) I don't see...

Homework Statement Hi, I've been working on this for a while but I just can't seem to figure this out. I have to solve a problem regarding a one-dimensional two-particle wavefunction psi(x1, x2, t) that is normalized at t=0, and the particles are not in spin. I have to show that the...

Hi There! Being direct to the point: Does normalization removes singularities? Such as infinite. I came up with this question because, while I was working with a not normalized function, I reached a very strange result. There are two points where the probability tends to infininte...

I have just begun using the 1-D Schrodinger Equation in my quantum mechanics course. We are assuming the potential, V, is solely a function of x (V(x)). I have been examining the solution to the differential equation through separation of variables. Ψ(x,t) = ψ(x)φ(t) (Assuming Ψ(x,t) is...

Which of the following are true in curved spacetime? \int d^4 x \delta^4(x - x_0) = 1 (1) \int d^4 x \sqrt{-g} \delta^4(x - x_0) = 1 (2) I think the first one is incorrect in curved spacetime, or in general when the metric is non-constant. I would argue this by saying that the delta...

hello all how can I determine the normalizing factor for arandom integers between tow values?

Homework Statement I have normalized the following function: Q=\int (1-y^2) dx dy Homework Equations using the expression for the normalization \vert N \vert ^2 \vert \int Q^* Q dx dy \vert^2 =1 The Attempt at a Solution then I obtained \int Q^* Q dx dy = x (y-...

I just want to make sure I understand this point: The eigenfunctions of the hydrogenic Hamiltonian are \varphi_{nlm}=R_{nl}Y^{m}_{l} If I need to find the probability of finding the electron in the nucleus (in r<R0), and I use the normalized R_{nl}, can I simply calculate the integral...

Homework Statement Consider the electron wave function where x is in nm: psi(x)=cx |x|<= 1nm & c/s |x| => 1 nm Determine the normalization constant c Homework Equations integral(|psi(x)|^2) dx=1 between infinity and negative infinity The Attempt at a Solution this may...

Homework Statement In a double-slit experiment, the slits are on the y-axis and the electrons are detected on a vertical screen. When only slit #1 is open, the amplitude of the wave which gets through is \psi(y,t) = A \exp^{-y^2} \exp^{-i((ky-\omega t)} when only slit #2 is open...