Expectation Definition and 689 Threads

Homework Statement Calculate the expectation value for the z component of angular momentum (operator is (h/i)(d/dx)) for the function sinx*e^(ix). Homework Equations I think the only one relevant is the expectation value: <a> = integral[psi*(a)psi] / integral[psi*psi] where psi* is...

Hi, I find a lot of the time in QM i have been calculating things blindly. Take the expectation value for instance. I have worked this out in integral form plenty of times, but haven't really understood why I'm doing what I'm doing. I looked up wikipedia and apparently, for a measurable...

Homework Statement Psi(x) = Ax -a<x<a I am trying to find the probability that my measured momentum is between h/a and 2h/a Homework Equations I have normalized A= sqrt(3/(2a^3)) I know that if I was finding the expected momentum I would use \int\Psi * p \Psi dx The...

Homework Statement I am familiar with the following kind of conditional expectation expression: \mathbb{E}[Y|X=x], where X and Y are random variables. I am wondering what the following conditional expectation stands for: \mathbb{E}[Y|X] How these two are related? How the second...

In QFT expressions such as these hold: real scalar: \Delta_F(x-x')\propto\langle 0| T\phi(x)\phi(x')|0\rangle 4-spinor S_F(x-x')]\propto\langle 0| T\psi(x)\bar{\psi}(x')|0\rangle where T is the time-ordering operation and the proportionality depends on the choice of normalization...

I'm not sure why PhysicsForums.com isn't displaying my latex properly so I have attached a PDF of the question. Homework Statement Show that, for a 3D wavepacket, \frac{d\langle x^2 \rangle}{dt} $=$ \frac{1}{m}(\langle xp_{x} \rangle+\langle p_{x}x \rangle) The Attempt at a...

Hi, I have the following problem: Suppose you have a coin that has chance p of landing heads. Suppose you flip the coin n times and let X denote the number of 'head runs' in n flips. A 'head run' is defined as any sequence of heads. For example the sequence HHTHHHHHTTTTHHTHT contains 4 head...

Show that (d/dt)<x^2>=(1/m)(<x(p_x)>+<(p_x)x>) For a three dimensional wave packet Homework Equations 1. <O>=Int_v(d^3r)(psi*Opsi), where O is some operator Ehrenfest Theorem: 2. ihbar(d/dt)<O>=<[O,H]>+<(partial)(d/dt)O>, H is a hamiltonian. The Attempt at a Solution I...

Homework Statement Suppose X ~ uniform (0,1) and the conditional distribution of Y given X = x is binomial (n, p=x), i.e. P(Y=y|X=x) = nCy x^{y} (1-x)^{n-y} for y = 0, 1,..., n. Homework Equations FInd E(y) and the distribution of Y.The Attempt at a Solution f(x) = \frac{1}{b-a} = \frac{1}{1-0}...

Show that the expectation value of Lz is -2h for the radial wavefunction Y2,-2. ? Can someone do this?

Homework Statement Show that the expectation value of the Coulomb potential v(\vec{r_1},\vec{r_2})=\frac{e^2}{|\vec{r_1}-\vec{r_2}|}, between two electrons depends on the relative orientation of spin of the two electrons. Assume each electron is in the product state form...

Is there any way of proving <p> = 0 for a discrete (bound) state given it's wave function? I've seen proofs using the hermitian properties of p but I'm interested in proving that the integral of Psi*(x) Psi'(x) is identically zero regardless of Psi(x) as long as it's a solution of Schroedinger's...

hi, not strictly homework as my course doesn't get going again for a couple of weeks yet, but suppose I have a system with quantum number l=1 in the angular momentum state u = \frac{1}{\sqrt{2}} \left(\begin{array}{cc}1\\1\\0\end{array}\right) and I measure Lz, the angular momentum component...

Ok I am not sure if I should put this question in the homework category of here but it’s a problem from schaums outline and I know the solution to it but I don’t understand the solution 100% so maybe someone can explain this to me. Let X and Y be defined by: \begin{array}{l} X = \cos \theta...

If I have H=p^2/2m+V(x), |a'> are energy eigenkets with eigenvalue E_{a'}, isn't the expectation value of [H,x] wrt |a'> not always 0? Don't I have that <a'|[H,x]|a'> = <a'|(Hx-xH)|a'> = <a'|Hx|a'> - <a'|xH|a'> = 0 ? But if I calculate the commutator, I get: <a'|[H,x]|a'> = <a'|-i p \hbar /...

I've been struggling with this problem for more than 4 days now: Let A, B and C be exponential distributed random variables with parameters lambda_A, lambda_B and lambda_C, respectively. Calculate E [ B | A < B < C ] in terms of the lambda's. I always seem get an integral which is...

Let A be an observable (opeator), and we're assuming that for a given state psi(x), the value of A is given by A acting on psi(x), namely - A|psi>. Also we assume that - P(x) = |psi(x)|^2 So, I'de expect the Expectation value of A to be defined like so: <A> = Integral[-Inf:+Inf]{ P(x) A...

Homework Statement Calculate the expectation value of \hat{H}' in the state \psi(x,t=0). \hat{H}'=k(\hat{x}\hat{p}+\hat{p}\hat{x}) \psi(x,t=0)=A(\sqrt{3}i\varphi_{1}(x)+\varphi_{3}(x)), where A=\frac{1}{2} Homework Equations The Attempt at a Solution I know it's found by...

I have small question computing vacuum expectation values here http://www.cns.gatech.edu/FieldTheory/extras/SrednickiQFT03.pdf" from Mark Srednicki. My problem is with equation 210 on the pdf page 69. In the second line of 210, where does the second term come from? Z(J) and W(J) are defined...

Homework Statement I have E(a) = 0, E(b) = x but E(|a+b|)=?? where E is the expectations operator and x is a known constant which is greater than zero. Homework Equations Any one know how I would go about determining E(|a+b|)?

Homework Statement Say, it is known that E_X[f(X)] = E_X[g(X)] = a where f(X) and g(X) are two functions of the same random variable X. What is the relationship between f(X) and g(X)? Homework Equations The Attempt at a Solution My answer is f(X) = g(X) + h(X) where E_X[h(X)] =...

Homework Statement Hello, have a stats question I am hoping you guys can help with. The expectation of a function g of a random variable X is: E[g(X)] = \int^{\infty}_{-\infty} g(x)fx(x)dx where fx is the pdf of X. For example, the particular expectation I am considering right now...

In the book "The mathematic of Gambling", the author considers a fair coin with 50% getting head and 50% for tail. The expectation of such coin, of course, will be zero. Here is what I read from the text, it reads Consider the fair game example mentioned earlier in the chapter (fair coin)...

Homework Statement A wavefunction of angular momentum states is given: \psi = \frac{1}{\sqrt{7}}|1,-1\rangle + \frac{\sqrt{35}}{7}|1,0\rangle+\sqrt{\frac{1}{7}}|1,1\rangle Calculate \langle \psi| L_{\pm} |\psi \rangle and \langle 1,1|L_+^2|\psi\rangle3. Attempt at a solution. If the...

Quantum Mechanics "Expectation" Homework Statement 1. Calculate the expectation value <p_{x}> of the momentum of a particle trapped in a one-dimensional box. 2. Find the expectation value <x> of the position of a particle trapped in a box L wide.Homework Equations \psi...

hello! can any1 please help me with the following proofs? thanks let X and Y be random variables. prove the following: (a) if X = 1, then E(X) = 1 (b) If X ≥ 0, then E(X) ≥ 0 (c) If Y ≤ X, then E(Y) ≤ E(X) (d) |E(X)|≤ E(|X|) (e) E(X)= \sumP(X≥n)

Homework Statement I am trying to derive for myself the velocity of the expectation value from the information given, specifically that <x> = \int_{-\infty}^{\infty}x|\Psi (x,t)|^2 dt (1) Eq (1) can be transformed into, \frac{d<x>}{dt} =...

Homework Statement What are the possible results and their probabilities for a system with l=1 in the angular momentum state u = \frac{1}{\sqrt{2}}(1 1 0)? What is the expectation value? ((1 1 0) is a vertical matrix but I can't see how to format that) Homework Equations The...

How to compute E[X|Y1,Y2]? Assume all random variables are discrete. I tried E[X|Y1,Y2] = \sum_x{x p(x|y1,y2) but I'm not sure how to compute p(x|y1,y2] = \frac{p(x \cap y1 \cap y2)}{p(y1 \cap y2)} If it is correct, how can I simplify the expression if Y1 and Y2 are iid?

Homework Statement Find the expectation value of x (Find <x>) given the wave function: \psi(x)=[sqrt(m*alpha)/h_bar]e^[(-m*alpha*|x|)/(h_bar)^2] This wave function represents the single bound state for the delta-function potential. It's the solution to the shrodinger equation given the...

Does anybody help me how to find the average (expectation) of terms involving double summation? Here is the equation which I'm trying solve. [\tex]E\Big[2\sum_{k=0}^{N-2}\sum_{j=k+1}^{N-1}f(k,j)\cos[2\pi(j-k)t-\theta_{k,j}]\Big][\tex] where f(k,j) and [\tex]\theta_{k,j}[\tex] are some...

Homework Statement Consider a hydrogen atom whose wave function at time t=0 is the following superposition of normalised energy eigenfunctions: Ψ(r,t=0)=1/3 [2ϕ100(r) -2ϕ321(r) -ϕ430(r) ] What is the expectation value of the angular momentum squared? Homework Equations I know...

Homework Statement If an electron is in an eigen state with eigen vector : [1] [0] what are the expectation values of the operators S_{x}, and S_{z} Interpret answer in terms of the Stern-Gerlach experiment. The Attempt at a Solution Im not too sure how to calculate the...

1. If X is uniform distributed in (0,pi), what is E(X|sinX)? 2. Suppose X and Y are Gaussian random variables N(0,sigma_x) and N(0,sigma_y). what is the distribution of E(X-Y|2X-Y) Can anyone help? thanks

Do we have to use normalised wavefunction to calculate the expectation and probability of finding the particle? If yes, why?

I'm trying to calculate the expectation value of the momentum squared (p^2) of the harmonic oscillator ground state. The integral involves the second derivative of a Gaussian (exponential of a negative squared term) Then the integral involves, after working it out, an x^2 term times...

In a paper in Physical Review A, the author discusses a wave function for one particle, Ψ(r,t), where r is the position vector. He writes "The probability distribution for one-particle detection at a point r is given by |<r|Ψ >|2 ". Is that correct? The above expression looks, to me...

Hi I'm going through some presentation material and i can't understand how the following has been derived \sum^{n}_{j=1} \mathbb{E}[ ln(1 +K_{j})] = n \mathbb{E}[ln(1+K_{1})] Could someone point me in the right direction on why this makes sense ? Thanks

Homework Statement 8. Suppose that X and Y are independent continuous random variables, and each is uniformly distributed on the interval [0,1] (thus the pdfs for X and Y are zero outside of this interval and equal to one on [0,1]). (a) Find the mean and variance for X+Y. (b) Calculate...

Homework Statement I need to find <x>, <x2>, <p>, and <p2> for a particle in the first state of a harmonic oscillator. Homework Equations The harmonic oscillator in the first state is described by \psi(x)=A\alpha1/2*x*e-\alpha*x2/2. I'm using the definition <Q>=(\int\psi1*Q*\psi)dx...

I'm looking at a question... The last part is this: find the expectation values of energy at t=0 The function that describes the particle of mass m is A.SUM[(1/sqrt2)^n].\varphi_n where I've found A to be 1/sqrt2. The energy eigenstates are \varphi_n with eigenvalue E_n=(n + 1/2)hw...

ok. this is an easy enough thing to prove in one dimension but my question seems to be 3 dimensional and it's causing me some hassle: show the expectation value of the kinetic energy in a bound state described by the spherically symmetric wavefunction \psi_T(r) may be written \langle...

I have two random variables Y and X and Y is dependent of X, though X is not the only source of variability of Y. With fixed X=x, Y(x) follows gaussian law. X also follows gaussian law. In what cases can I move from E[ Y(X) ] to E[ Y(E(X))] someone has any idea? is there a text...

Hello, this is just a general question, how is <x^2> evaluated, if <x> = triple integral of psi*(r,t).x.psi(r,t).dr (this is the expectation value of position of wavepacket) Is it possible to square a triple integral? Is <x^2> the same as <x>^2 ? I'm only wondering how the squared works...

If the expectation of some observable is constant then can it be measured at Lab.

I've never seen an expectation value taken and would greatly appreciate seeing a step by step of how it is done. Feel free to use any wavefunction, this is the one I've been trying to do: In the case of \Psi=c1\Psi1 + c2\Psi2 + ... + cn\Psin And the operator A(hat) => A(hat)\Psi1 =...

I have been stuck at this calculation. There are two exponential distributions X and Y with mean 6 and 3 respectively. We need to find E[y-x|y>x] I keep getting it negative, which is clearly wrong. Anybody wants to try it?

Kalman Filter - Covariance Matrix Kalman Filter Problem Homework Statement I have the following expectation formula: P_k=E\{\left[(x_k-\hat{x}^-_k)-K_k(H_k x_k+v_k-H_k \hat{x}^-_k)\right]\left[(x_k-\hat{x}^-_k)-K_k(H_k x_k+v_k-H_k \hat{x}^-_k)\right]\}2. The attempt at a solution I'm told...

Find the time dependence of the expectation value <x> in a quantum harmonic oscillator, where the potential is given by V=\frac{1}{2}kx^2 I'm assuming some wavefunction of the form \Psi(x,t)=\psi(x) e^{-iEt/\hbar} When I apply the position operator, I get: <x>=\int_{-\infty}^\infty...