Expectation Definition and 689 Threads

hi there. currently looking at the two conditions that must be met for a process to be wide sense stationary. The first constion is: E[X(t)] = constant what exactly does this mean??isn't is obvious that any random variable (with fixed time) will always yield a constant expextation. I...

I'm still really confused on how to go about calculating this for non eigenstates. I'm trying to do the problem below, and am wondering how to go about it. \Psi (x,0) = A (1-2 \sqrt {\frac{m \omega}{\hbar}} x)^2 e^ {-\frac{m \omega x^2}{2 \hbar}} So I can't calculate the expectation...

Problem 1.17 in griffiths gives, at time t = 0, the state psi =A(a^2-x^2) for -a to a, and 0 otherwise. It asks then to find the expected value of momentum p at 0 and also the uncertainty in p. How do I do this? The only way momentum is defined is md<x>/dt, and since the state is only for time...

In one of the proofs I'm reading, I need to show that the \phi(X) that will minimize E[Y - \phi(X)]^{2} is \phi(X) = E(Y|X) the proof is shown to proceed as follows: E[Y - \phi(X)]^{2} =E[(Y - E(Y|X)) + (E(Y|X) - \phi(X))]^{2} expanding, we have =E[(Y - E(Y|X))^{2} + 2(Y - E(Y|X))(E(Y|X) -...

I need help in solving the following problem: Let X be uniformly distributed over [0,1]. And for some c in (0,1), define Y = 1 if X>= c and Y = 0 if X < c. Find E[X|Y]. My main problem is that I am having difficulty solving for f(X|Y) since X is continuous (uniform continuous over [0,1])...

Any hints on how to solve for E(Y|X) given the ff: Suppose U and V are independent with exponential distributions f(t) = \lambda \exp^{-\lambda t}, \mbox{ for } t\geq 0 Where X = U + V and Y = UV. I am having difficulty finding f(Y|X)... Also, solving for f(X,Y), I am also having difficulty...

Is it possible to solve for E(Y) and var (Y) when I am only given the distribution f(Y|X)? I can solve for E(Y|X). But is it possible to find E(Y) and var(Y) given only this info?

Is it true that all expectation values must be real? So if I get an imaginary value, does it mean I made a mistake? Or it doesn't matter and I can just take the absolute value of the expectation? The momentum operator has an 'i' in it. But after doing, Psi*[P]Psi, I have an expression with 'i'...

I have calculated the expectation value of a particle in a box of width a to be a/2. The wavefunction of the particle is: N Sin(k_n x) Exp[-i \frac{E_n t}{\hbar}] Now, in the first excited state with k_n equal to 2\pi / a the position probability density peaks at a/4 and 3a/4 but is zero...

I need to calculate <x^n> and <p^n> for psi(x)=exp(-ax^2/2) for n even. For <x^n>: <x^n>=integral(exp(-ax^2)*x^n )dx from -inf to +inf then i use integration by parts to get an infinite series and i use a formula to find the finite sum of the series =[exp(-ax^2)*x^(n+1)/((n+1-2a*(n+1)^2)]...

hi all can sombody show me the way I could get the square expectation value http://06.up.c-ar.net/03/fd4f.jpg for a particle in a box where the answer is given to us : http://06.up.c-ar.net/03/87d0.jpg

I need help getting started on this problem: A free particle moving in one dimension is in the initial state \Psi(x,0) . Prove that <\hat{p}> is constant in time by direct calculation (i.e. without recourse to the commutator theorem regarding constants of the motion). Our professor...

Hey, I've got this problem from Peskin & Schroeder (chapter 15). I'm not particularly confident with functional integration, as I'm pretty new to it, and working through such a book by myself is pretty tricky in places. Well here goes The Wilson Loop for QED is defined as U_p(z, z)=\exp...

I have a wavefunction given by: \psi = \sqrt{\frac{2}{L}}\sin \frac{n\pi x}{L} With boundary conditions 0<x<L. When I compute the expectation value for the momentum like this: \overline{p_x} = \int_0^L \sqrt{\frac{2}{L}}\sin \frac{n\pi x}{L} \left(-i\hbar \frac{\partial}{\partial...

how do you find the expectation value <x> for the 1st 2 states of a harmonic oscillator?

Isn't consistently being inconsistent... consistency? Everything within it's own nature is consistent, and the human expectation and/or desire cannot change that to fit his scenario. Definitions of words in this world are lost in misconceptions. I often get made fun of for making these...

Hi.. i am doing this question for Probability Theory, to find E[x] of a continuous random variable E[x] = the integral from (0 to infinity) of 2x^2 * e^(-x^2) dx So I used integration by parts... u = x^2 du = 2xdx dv = e^(-x^2) <--- ahh... how do you integrate that. (it dosn't look like...

I found this question in a book: Two palyers A and B alternatively roll a pair of unbiased die. A wins if on a throw he obtain exactly 6 points, before B gets 7 points, B wining in the opposing event. If A begins the game prove that the probability of A winning is 30/61 and that the expected...

We have a particle in a harmonic oscillator potential. The eigenstates are denoted {|0>,|1>,...,|n>,...}. Initially the particle is in the state |s> = exp(-ipa)|0>, where p is the momentum operator. I need to find <x> as a function of time using the Heisenberg picture. The problem is, how do...

Hello everyone, This really has me stumped! The Washington state lottery has a new game called Zip Bingo. Every ticket costs $2 and consists of 2 regular Bingo cards with 35 call numbers. The prizes are as follows: Regular bingo on card 1: $2 Regular bingo on card 2: $3 Regular...

I need to find the momentum expectation value of the function in the attached picture. It is the function of the harmonic oscillator (first excited state). :confused: I know that the expectation value is the value that we measure with the highest probability if we measure the system. But...

I am new here and grateful to have found this site! I have a problem: The question is: Roll a fair die 3 times. Find the math expectation of the numerical sum of the outcomes of the rolls. I have no clue. I have looked over all notes, and I just don't "get it". Can someone help...

Hi, I have to find the expectation values of xp and px for nth energy eigenstate in the 1-d harmonic oscillator. If I know <xp> I can immediately find <px>since [x,p]=ih. I use the ladder operators a_{\pm}=\tfrac1{\sqrt{2\hslash m\omega}}(\mp ip+m\omega x) to find <xp>, but I get a complex...

What is the relationship between Expectations, Moments, and Autocorrelation. Can somone please please give me some examples? thanks

Hello, I have difficulty understanding the vacuum expectation: consider <0|A_{mu}|0>, we can understand it as the possibility ampitude of a photon turn into vacuum(although 0 in common), but in the spontaneous of gauge symmetry, we should understand <0|A_{mu}|0> as the strength of a...

Hi, could anyone tell me how one would show that the expectation value of a anti-Hermitian operator is a pure imaginary number? Thanks.

X~N(0,1), Y=X^2~\chi^2(1), find E(XY). My thoughts are in the following: To calculate E(XY), I need to know f(x,y), since E(XY)=\int{xyf(x,y)dxdy}. To calculate f(x,y), I need to know F(x,y), since f(x,y)=d(F(x,y)/dxdy. F(x,y)=P(X\leq x, Y\leq y) \\ =P(X\leq x, X^{2} \leq...

Two quick ones :) Hi, two questions: 1) How can I find the expectation value of the x-component of the angular momentum, \langle L_x \rangle, when I know \langle L^2 \rangle and \langle L_z \rangle? 2) Say, I have a state |\Psi \rangle and two operators A and B represented as matrices...

This is the problem: Calculate: \newcommand{\mean}[1]{{<\!\!{#1}\!\!>}} \frac {d \mean{p}}_{dt} Here's a few more points to keep in mind... (A) The assumption is that <p> is defined as: \newcommand{\mean}[1]{{<\!\!{#1}\!\!>}} \mean{p} = -i \hbar \int \left( \psi^* \frac...

Given the wave function: \psi (x,t) = Ae^ {-\lambda \mid x\mid}e^ {-(i ) \omega t} where A, \lambda , and \omega are positive real constants I'm asked to find the expectation values of x and x^2. I know that the values are given by <x> = \int_{-\infty}^{+\infty} x(A^2)e^...

I want to find the expectation value \langle x^2 \rangle in some problem. To do this I make a change-of-variable, \xi = \sqrt{\frac{m\omega}{\hslash}}x, and compute the expectation value \langle \xi^2 \rangle like this: \langle \xi^2 \rangle = \int\xi^2\vert\psi(\xi)\vert^2d\xi...

When I'm in a dimension higher than 1, do I need to integrate over all space (V) or only the x axis? Thanks in advance.

I had thought that the expectation value would be the same...whether you did it in momentum space or position space. Could someone explain what is going on in this particular problem? \psi (x) = \sqrt{b} e^{-b |x| + i p_0 x / \hbar } Taking the Fourier transform, I can get this...

If the expectation value <x> of a particle trapped in a box L wide is L/2, which means its average position in the middle of the box. Find the expectation value <x squared>. How do I go about doing this? I am really confused.

Here is a question that I have found in my quantum text which I have been thinking about for a few days and am unable to make sense of. If there is an operator A whose commutator with the Hamiltonian H is the constant c. [H,A]=c Find <A> at t>0, given that the system is in a normalized...

Expectation value problem pleasezzz help ASAP Hi Everyone, I have a problem on one of my problems in the quantum course. I need tofind the expectation values <x>,<x^2>, <p> & <p^2> for the function e^(-(x-xo)^2/2k^2) please email me if you need theformulaes.. i have them but i...

I am having trouble applying this concept to simple things. Like a die where we let s be the number of spots shown by a die thrown at random. How could I compute the expectation value of s? And how would I compute the mean square deviation. Would the expectation value just be <s>=1/N...

Playing video poker, 9/6 Jacks or Better, has an expected return, computer calculated, of 99.54% with perfect play. Many players today certainly regard mathematical facts as much more useful than a rabbit's foot. They want to know the odds. During a progressive game, where the value of the...

Can anyone let me know the estimator for the expectaiion of X^Y. X and Y are iid random variables, and their expectation are E(X) and E(Y) respectively. Thank you.