What is Expectation: Definition and 688 Discussions

Expectation damages are damages recoverable from a breach of contract by the non-breaching party. An award of expectation damages protects the injured party's interest in realising the value of the expectancy that was created by the promise of the other party. Thus, the impact of the breach on the promisee is to be effectively "undone" with the award of expectation damages.The purpose of expectation damages is to put the non-breaching party in the position it would have occupied had the contract been fulfilled. Expectation damages can be contrasted to reliance damages and restitution damages, which are remedies that address other types of interests of parties involved in enforceable promises.The default for expectation damages are monetary damages which are subject to limitations or exceptions (see below)
Expectation damages are measured by the diminution in value, coupled with consequential and incidental damages.

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  1. S

    What are the expectation values for position and momentum in states Ψ0 and Ψ1?

    For question 2.2: <Ψ0|p|Ψ0> = ∫Ψ0 -iħ d/dx(Ψ0) =M Using Integration by parts i get: M = -Ψ0 iħ d/dx(Ψ0) (assuming hilbert space) Implying the expectation values for momentum are zero , however i get all the expectation values are zero for x and momentum in both states which makes no sense :(
  2. E

    Expectation value of operators and squeezing in the even cat state

    I started and successfully showed that the expectation of X_1 and X_2 are zero. However the expectation value of X1^2 and X2^2 which I am getting is <X1^2> = 0.25 + \alpha^2 and <X2^2> = 0.25. How do I derive the given equations?
  3. J

    Expectation of Momentum in a Classical (Infinite) Potential Well

    Okay so I begin first by mentioning the length of the well to be L, with upper bound, L/2 and lower bound, -L/2 and the conjugate u* = Aexp{-iz} First I begin by writing out the expectation formula: ## \langle p \rangle = \int_{\frac{L}{2}}^{ \frac{L}{2} } Aexp(-iu) -i \hbar \frac{ \partial }{...
  4. L

    I Expectation value of the occupation number in the FD and BE distributions

    In the derivation of the Fermi-Dirac and Bose-Einstein distributions, we compute the Grand Partion Function ##Q##. With ##Q##, we can compute the espection value of the occupation number ##n_{l}##. This is the number of particles in the same energy level ##\varepsilon _{l}##. The book I am...
  5. Mentz114

    B Expectation of the number of successes in Bernoulli trial

    I'm trying calculate the expected number of steps in one node in a random walk , ##\langle s\rangle=\sum sp^s##. By deduction I have a possible solution (for rational probabilities ##p=n/m,\ n< m##) in ##\bar{s}=\langle s\rangle= nm/(m-n)^2##, which looks pretty weird but I have not found a...
  6. J

    I Time evolution of an expectation value

    Watching Dr. Susskind show how to find the time evolution of the average of an observable K, he writes: I can not for the life of me figure out he derived it, and he also did something which I found terribly annoying throughout which is set hbar to 1, so after steps you lose where the hbar...
  7. astrocytosis

    Darwin term in a hydrogen atom - evaluating expectation values

    Homework Statement Homework Equations VD= -1/(8m2c2) [pi,[pi,Vc(r)]] VC(r) = -Ze2/r Energy shift Δ = <nlm|VD|nlm> The Attempt at a Solution I can't figure out how to evaluate the expectation values that result from the Δ equation. When I do out the commutator, I get p2V-2pVp+Vp2. This...
  8. S

    B Expectation of probability density function

    E(X) of probability density function f(x) is \int x f(x) dx E(X2) of probability density function f(x) is \int x^2 f(x) dx Can I generalize it to E(g(x)) of probability density function f(x) = \int g(x). f(x) dx ? I tried to find E(5 + 10X) from pdf. I did two ways: 1. I found E(X) then using...
  9. redtree

    I Expectation value of Fourier conjugates

    I understand that the Uncertainty Principle relates the variances of Fourier conjugates. I am having trouble finding: 1) the mathematical relationship between the expectation values of Fourier conjugates generally; 2) and then specifically for a normalized Gaussian. Any suggestions or insights?
  10. learn.steadfast

    I Hermitian and expectation values.... imaginary?

    I've been studying quantum mechanics, and working problems to get a feel for expectation values and what causes them to be real. I was working the problem of finite 1D wells, when I came across a situation I did not understand. A stationary state solution is made up of a forward and reverse...
  11. D

    How to find the expectation value of cos x

    Homework Statement If x is a continuous variable which is uniformly distributed over the real line from x=0 to x -> infinity according to the distribution f (x) =exp(-4x) then the expectation value of cos 4x is? Answer is 1/2 Follow· 01 Request Homework Equations the expectation value of any...
  12. L

    Help with finding the expectation value of x^2

    The question is as follows: A particle of mass m has the wave function psi(x, t) = A * e^( -a ( ( m*x^2 / hbar) +i*t ) ) where A and a are positive real constants. i don't know how to format my stuff on this website, so it may be a bit harder to read. Generally when i write "int" i mean the...
  13. Technon

    I Expectation Value of f(x): Physical Meaning

    The expectation value of any function ##f(x)## is given by <f(x)>= \int_{-\infty}^{\infty}f(x)\psi^2(x) dx But what is ##f(x)## actually? In a physical sense. For example if ##f(x)=x## or ##f(x)=x^2##, what do these functions represent on a physical level?
  14. M

    Find the spinor-state for a given expectation value

    Homework Statement Let ##\vec{e}\in\mathbb{R}^3## be any unit vector. A spin ##1/2## particle is in state ##|\chi \rangle## for which $$\langle\vec{\sigma}\rangle =\vec{e},$$ where ##\vec{\sigma}## are the Pauli-Matrices. Find the state ##|\chi\rangle## Homework Equations :[/B] are all given...
  15. F

    I Expectation Maximization (EM) : find all parameters

    I am tackling a technique to determine the parameters of a Moffat Point Spread Function (PSF) defined by: ## \text {PSF} (r, c) = \bigg (1 + \dfrac {r ^ 2 + c ^ 2} {\alpha ^ 2} \bigg) ^ {- \beta} ## with the parameter "(r, c) =" line, column "(not necessarily integers). The observation of a...
  16. Faizan Samad

    Calculate the expectation value of V from Ehrenfest's theorem

    Homework Statement I have a general question how I calculate the expectation value of V (potential energy) with Ehrenfest’s theorem. Do I have to integrate d<p>/dt with respect to d<x>. Also if the potential is symmetric (even) would that mean the expectation value of the potential is 0...
  17. Warda Anis

    Expectation value <p> of the ground state of hydrogen

    Homework Statement How should I calculate the expectation value of momentum of an electron in the ground state in hydrogen atom. Homework Equations The Attempt at a Solution I am trying to apply the p operator i.e. ##-ihd/dx## over ##\psi##. and integrating it from 0 to infinity. The answer I...
  18. gasar8

    Which particles can have vacuum expectation values and why?

    Homework Statement Can someone explain to me what particles (fermions, scalar/vector bosons, gravitons, ...) can have their vacuum expectation values and why? Which components of these fields can have VEV-s? The Attempt at a Solution I am assuming only scalar boson fields have it (like Higgs...
  19. thariya

    A Independence of Operator expectation values

    Hi! I want to know under what conditions the operator expectation values of a product of operators can be expressed as a product of their individual expectation values. Specifically, under what conditions does the following relation hold for quantum operators (For my specific purpose, these are...
  20. Matt Chu

    Time Derivative of Expectation Value of Position

    Homework Statement I want to prove that ##\frac{\partial \langle x \rangle}{\partial t} = \frac{\langle p_x \rangle}{m}##. Homework Equations $$i\hbar \frac{\partial \Psi}{\partial t} = -\frac{\hbar^2}{2m} \frac{\partial^2 \Psi}{\partial x^2} + V \Psi$$ The Attempt at a Solution [/B] So...
  21. T

    Expected bounds of a continuous bi-variate distribution

    Homework Statement [/B] ##-1\leq\alpha\leq 1## ##f(y_1,y_2)=[1-\alpha\{(1-2e^{-y_1})(1-2e^{-y_2})\}]e^{-y_1-y_2}, 0\leq y_1, 0\leq y_2## and ##0## otherwise. Find ##V(Y_1-Y_2)##. Within what limits would you expect ##Y_1-Y_2## to fall? Homework Equations N/A The Attempt at a Solution...
  22. K

    I What is the correct expectation value for this game with redraw?

    Hi all, I am creating a game for fun, which need some math skill to work out the chance of winning and the way to keep the banker never lose. The configuration of the game is like this: five boxes marked no.1, no.2, no.3, no.4 and no.5; there are many balls in different color in each box. For...
  23. F

    Is there an optimal distance between measurements for regression

    Suppose I am trying to approximate a function which I do not know, but I can measure. Each measurement takes a lot of effort. Say the function I am approximating is ##y=f(x)## and ##x \in [0,100]## Supose I know the expectation and variance of ##f(x)##. Is there a way to compute the confidence...
  24. S

    I Expectation for the Harmonic Oscillator ( using dirac)

    I've been trying to form a proof using , using majorly dirac notation.There has been claims that its much better to use in QM. The question i wanted to generally show that the expected value is Zero for all odd energy levels.I believe i have solved the question but I am a bit Iffy about a step...
  25. renec112

    Free particle: expectation of x for all time with Ehrensfest

    Hello physics forums. I'm trying to solve an old exam question. Would love your help. Homework Statement A free particle in one dimension is described by: ## H = \frac{p^2}{2m} = \frac{\hbar}{2m}\frac{\partial^2}{\partial x^2}## at ##t = 0## The wavefunction is described by: ## \Psi(x,0) =...
  26. renec112

    Expectation value of raising and lower operator

    I am practicing old exams. I tried my best but looking at an old and a bit unreliable answer list, and i am not getting the same result. Homework Statement At time ##t=0## the nomralized harmonic oscialtor wavefunction is given by: ## \Psi(x,0) = \frac{1}{\sqrt{3}}(\psi_0(x) + \psi_1(x) + i...
  27. J

    Expectation Value of a Stochastic Quantity

    Homework Statement I'm working on a process similar to geometric brownian motion (a process with multiplicative noise), and I need to calculate the following expectation/mean; \langle y \rangle=\langle e^{\int_{0}^{x}\xi(t)dt}\rangle Where \xi(t) is delta-correlated so that...
  28. C

    Expectation values and probabilities for spinors in a well

    Working on a homework at the moment involving spinors. The algebra isn't hard at all, I just want to make sure my understanding is right and I'm not doing this incorrectly. 1. Homework Statement An electron in a one-dimensional infinite well in the region 0≤x≤a is described by the spinor ψ(x)...
  29. D

    Expectation value of position

    Homework Statement Show that, for a general one-dimensional free-particle wave packet $$\psi (x,t) = (2 \pi h)^{-1/2} \int_{-\infty}^{\infty} exp [i (p_x x - p_x^2 t / 2 m)/h] \phi (p_x) dp_x$$ the expectation value <x> of the position coordinate satisfies the equation $$<x> = <x>_{t=t_0}...
  30. S

    Expectation Value and Probabilities of Spin Operator Sy

    Homework Statement (a) If a particle is in the spin state ## χ = 1/5 \begin{pmatrix} i \\ 3 \\ \end{pmatrix} ## , calculate the expectation value <Sy>(b) If you measured the observable Sy on the particle in spin state given in (a), what values might you get and what is the probability of...
  31. renec112

    QM: expectation value and variance of harmonic oscillator

    Homework Statement A particle is moving in a one-dimensional harmonic oscillator, described by the Hamilton operator: H = \hbar \omega (a_+ a_- + \frac{1}{2}) at t = 0 we have \Psi(x,0) = \frac{1}{\sqrt{2}}(\psi_0(x)+i\psi_1(x)) Find the expectation value and variance of harmonic oscillator...
  32. D

    Expectation Value of Q in orthonormal basis set Psi

    Homework Statement Suppose that { |ψ1>, |ψ2>,...,|ψn>} is an orthonormal basis set and all of the basis vectors are eigenvectors of the operator Q with Q|ψj> = qj|ψj> for all j = 1...n. A particle is in the state |Φ>. Show that for this particle the expectation value of <Q> is ∑j=1nqj |<Φ|...
  33. Mehmood_Yasir

    I Conditional Expectation Value of Poisson Arrival in Fixed T

    Assume a Poisson process with rate ##\lambda##. Let ##T_{1}##,##T_{2}##,##T_{3}##,... be the time until the ##1^{st}, 2^{nd}, 3^{rd}##,...(so on) arrivals following exponential distribution. If I consider the fixed time interval ##[0-T]##, what is the expectation value of the arrival time...
  34. TheBigDig

    Expectation value of mean momentum from ground state energy

    1. The problem statement Consider a particle of mass m under the action of the one-dimensional harmonic oscillator potential. The Hamiltonian is given by H = \frac{p^2}{2m} + \frac{m \omega ^2 x^2}{2} Knowing that the ground state of the particle at a certain instant is described by the wave...
  35. RJLiberator

    Expressing expectation values of a particle moving in a periodic potential

    Homework Statement A particle moving in a periodic potential has one-dimensional dynamics according to a Hamiltonian ## \hat H = \hat p_x^2/2m+V_0(1-cos(\hat x))## a) Express ## \frac{d <\hat x>}{dt}## in terms of ##<\hat p_x>##. b) Express ## \frac{d <\hat p_x>}{dt}## in terms of ##<sin(\hat...
  36. T

    Expectation of energy for a wave function

    Homework Statement At ##t = 0##, a particle of mass m in the harmonic oscillator potential, ##V(x) = \frac1 2 mw^2x^2## has the wave function:$$\psi(x,0)=A(1-2\sqrt\frac{mw} {\hbar} x)^2e^{\frac{-mw}{2\hbar}x^2}$$ where A is a constant If we make a measurement of the energy, what possible...
  37. J

    Find the expectation from probability

    Homework Statement Assume that in a traffic junction, the cycle of the traffic signal lights is 2 minutes of green (vehicle does not stop) and 3 minutes of red (vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected...
  38. Y

    I Expectation value of energy in TISE

    If Eψ = Hψ, then why is expected energy ∫ψ*Hψ dx? It makes more sense if I see the ψ on the right side of H as the ψ in ∫Q(ψ*ψ) dx, where Q is some quantity we want to measure the expectation of. But if true, then since H is defined as (h2/2m) (d2/dx) + V, then what does it mean to calculate...
  39. I

    Calculate expectation value of entangled 2 state system?

    Homework Statement Homework Equations I know that there are two eigenstates of the operator C: |B> = (1 0) as a column vector with eigenvalue 1 |R> = (0 1) also a column vector with eigenvalue -1 The Attempt at a Solution My work is shown here: If anyone could point me in the right...
  40. A

    I Help with an expectation value formula

    Imagine a particle in an equally weighted superposition of being located in three distant regions P, Q, and R, and imagine you stand in region P with a measuring device. The probability of finding the particle there is 1/3. Now imagine a large number N of particles prepared in that same state...
  41. redtree

    B The expectation value of superimposed probability functions

    I apologize for the simplicity of the question (NOT homework). This is a statistical question (not necessarily a quantum mechanical one). If I have an initial probability function with an associated expected value and then a second probability function is superimposed on the initial...
  42. W

    Quantum Mechanics: Expectation values (Griffiths)

    Homework Statement A few questions: Q1) How does 1.29 flow to 1.30 and 1.31? How was the integral-by-parts done? Q2) The author states that <v> = d<x>/dt represents the expectation value of velocity. What does this actually mean? I tried to rationalise that d<x>/dt represented the velocity...
  43. i_hate_math

    I The symmetry argument and expectation value

    In 1D QM: I understand that if a given potential well, U(x), is symmetric about x = L, then the expectation value for operator [x] would be <x> = L. (I am not even entirely sure why this is, guessing that the region where x<L and x>L are equally probable) Is it possible to draw conclusion...
  44. D

    I Factorising expectation values

    Hi. I came across the following in the solution to a question I was looking , regarding expectation values of momentum in 3-D < p12p22p32 > = < p12 > < p22 > <p32 > ie. the expectation value has been factorised. I can't figure out why this is true and also why it doesn't apply to the following...
  45. binbagsss

    Probability , expectation, variance, cross-term vani

    Homework Statement I have a variable ##s_i## with probability distribution ##w(s_i)## ##(\Delta(s_i))^2## denotes the variance ##=<(s-<s>)^2>=<s^2>-<s>^2## I want to show ## \sum\limits_{i\neq j} <\Delta s_i> < \Delta s_j> =0 ## where ## < > ## denote expectation My book has: ## <\Delta...
  46. S

    Quantum Mechanics; Expectation value

    Homework Statement At t=0, the system is in the state . What is the expectation value of the energy at t=0? I'm not sure if this is straight forward scalar multiplication, surprised if it was, but we didn't cover this in class really, just glossed through it. If someone could walk me through...
  47. G

    Expectation values as a phase space average of Wigner functions

    Hi. I'm trying to prove that [\Omega] = \int dq \int dp \, \rho_{w}(q,p)\,\Omega_{w}(q,p) where \rho_{w}(q,p) = \frac{1}{2\pi\hbar} \int dy \, \langle q-\frac{y}{2}|\rho|q+\frac{y}{2}\rangle\,\exp(i\frac{py}{\hbar}) is the Wigner function, being \rho a density matrix. On the other hand...
  48. digogalvao

    Proof of expectation value for a dynamic observable

    Homework Statement Show that: d<A(q,p)>/dt=<{A,H}>, where {A,H} is a Poisson Bracket Homework Equations Liouville theorem The Attempt at a Solution <A>=Tr(Aρ)⇒d<A>/dt=Tr(Adρ/dt)=Tr(A{H,ρ}) So, in order to get the correct result, Tr(A{H,ρ}) must be equal to Tr({A,H}ρ), but I don't think I can...
  49. B

    Expectation values and commutation relations

    Homework Statement I am trying to calculate the expectation value of ##\hat{P}^3## for the harmonic oscillator in energy eigenstate ##|n\rangle## Homework EquationsThe Attempt at a Solution [/B] ##\hat{P}^3 = (i \sqrt{\frac{\hbar \omega m}{2}} (\hat{a}^\dagger - \hat{a}))^3 = -i(\frac{\hbar...
  50. B

    Time dependent expectation value problems

    Homework Statement Homework EquationsThe Attempt at a Solution I tried to solve (a), but i don't know which approach is right ((1) or (2)) and how to solve (b).[/B]
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