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.

View More On Wikipedia.org
Recent contents Top users
  1. Cocoleia

    Proving the expectation value of any eigenvalue function

    Homework Statement Homework Equations The Attempt at a Solution When I take the second formula, multiply by it's conjugate and then by x and do the integral of the first formula, I get 0, and not L/2, for <x>. Am I missing a formula ? The complex conjugate of the exponential part...
  2. N

    I Physical significance of a.σ in expectation -E(a.σ b.σ)?

    Admins: Please excuse my E and brackets in the title, and correct if possible. My questions are these, please: 1. What is the physical significance of (\hat{a}\cdot\boldsymbol{\sigma}_{1}) in \left\langle...
  3. S

    I Which ψ do I use for the Expectation Value ?

    I have to calculate the Expectation Value of an Energy Eigenstate : < En > The integral is ∫ ψ* En ψ dx I have : A ) ψ = √L/2 sin nπx/L , a single standing wave of the wave function B ) ψ = BsinBcosD , the wave function of the particle C ) ψ = ΣCn ψn = C , sum of all the...
  4. Kenneth Adam Miller

    I Expectation value with imaginary component?

    Hello, I'm a beginner at quantum mechanics. I'm working through problems of the textbook A Modern Approach to Quantum Mechanics without a professor since I am not going to college right now, so I need a brief bit of help on problem 1.10. Everything else I have gotten right so far, but I am...
  5. J

    MHB Conditional Expectation problem

    Q The amount of time (in minutes) that an executive of a certain firm talks on the telephone is a random variable having the probability density: $$f(x) = \begin{cases} \dfrac{x}{4}&\text{for $0 < x \le 2$}\\ \dfrac{4}{x^3}&\text{for $x > 2$}\\...
  6. Leechie

    Finding Spin Expectation Values At Any Time t > 0

    Homework Statement Write down a spinor that represents the spin state of the particle at any time t > 0. Use the expression to find the expectation values of ##S_x## and ##S_y## Homework Equations The particle is a spin-##\frac 1 2## particle, the gyromagnetic ratio is ##\gamma_s \lt 0##, and...
  7. F

    I Expectation of an operator (observable) how to calculate it

    Hello Forum, I understand that in order to calculate the average of a certain operator (observable), whatever that observable may be that we are interested in, we need to prepare many many many identical copies of the same state and apply the operator of interest to those identical state. By...
  8. andrewkirk

    I Validity of replacing X by E[X] in a formula

    Hello all. I am working on proving some theorems about Monte Carlo simulation and have proven a theorem that, in a certain formula, it is valid to replace a random variable in the denominator of a fraction by its expected value. I have been wondering whether this result can be generalised to...
  9. F

    Expected number of steps random walk

    Homework Statement Let w(1) = event of a random walk with right drift (p > q, p+q = 1) starting at 1 returns to 0 Let p(w(1)) = probability of w(1) Let S=min{t>=0:wt(1)=0} be the minimum number of steps t a walk starting from 1 hits 0. What is E[S|w(1)]? Homework Equations I know E[S|w(0)] = 0...
  10. M

    Wavefunction normalisation and expectation values

    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...
  11. F

    Optimal Stopping Strategy for Winning Game with Two Bells

    Homework Statement You are playing a game with two bells. Bell A rings according to a homogeneous poisson process at a rate r per hour and Bell B rings once at a time T that is uniformly distributed from 0 to 1 hr (inclusive). You get $1 each time A rings and can quit anytime but if B rings...
  12. D

    Expectation values of the quantum harmonic oscillator

    Homework Statement Show the mean position and momentum of a particle in a QHO in the state ψγ to be: <x> = sqrt(2ħ/mω) Re(γ) <p> = sqrt (2ħmω) Im(γ) Homework Equations ##\psi_{\gamma} (x) = Dexp((-\frac{mw(x-<x>)^2}{2\hbar})+\frac{i<p>(x-<x>)}{ħ})##The Attempt at a Solution I put ψγ into...
  13. Tspirit

    I Can the expectation of an operator be imaginary?

    Assume ##\varPsi## is an arbitrary quantum state, and ##\hat{O}## is an arbitrary quantum operator, can the expectation $$\int\varPsi^{*}\hat{O}\varPsi$$ be imaginary?
  14. A

    How to find expectation value for combined state?

    Homework Statement Given ##\psi = AR_{21}[BY_1^1 + BY_1^{-1} + CY_1^0]##, find ##\left<L_z\right>## and ##\left<L^2\right>##. (This is not the beginning of the homework problem, but I know my work is correct up to here. I am not looking for a solution, only an answer as to whether or not my...
  15. S

    Expectation value in coherent state

    Homework Statement In a coherent state ##|\alpha\rangle##, letting ##P(n)## denote the probability of finding ##n^{\text{th}}## harmomic oscillator state. Show that $$\displaystyle{\langle\hat{n}\rangle \equiv \sum\limits_{n}n\ P(n)=|\alpha|^{2}}$$ Homework Equations The Attempt at a...
  16. mertcan

    I Calculation of E[X|X>Y] for Exponential Random Variables

    Hi, Initially X and Y are exponential random variables with rate respectively $$\mu \lambda$$, and I am aware that E[X|X>Y] is obtained using joint distribution but I can not build up the integral structure, I intuitively think the result is just 1/mu, but I can not prove it to myself could you...
  17. N

    A Expectation operation for covariance calculation

    Hi, If E[wwH]=T, where w is a zero-mean row-vector and H is the Hermitian transpose then assuming that H is another random matrix, it holds that E[H w (H w)H] = T H HH or T E[H HH] ?? In other words, the expectation operation still holds as in the latter expression or vanishes as in the...
  18. F

    Expectation values linear harmonic oscillator

    hello :-) here is my problem...: 1. Homework Statement For a linear harmonic oscillator, \hat{H} = \frac{\hat{p}^2}{2m} + \frac{1}{2} m \omega^2x^2 a) show that the expectation values for position, \bar{x}, and momentum \bar{p} oscillate around zero with angular frequency \omega. Hint...
  19. perplexabot

    A Conditional expectation and covariance of function of RVs

    Hey all, I have been doing some math lately where I need to find the conditional expectation of a function of random variables. I also at some point need to find a derivative with respect to the variable that has been conditioned. I am not sure of my work and would appreciate it if you guys can...
  20. V

    Bohr frequency of an expectation value?

    Homework Statement Consider a two-state system with a Hamiltonian defined as \begin{bmatrix} E_1 &0 \\ 0 & E_2 \end{bmatrix} Another observable, ##A##, is given (in the same basis) by \begin{bmatrix} 0 &a \\ a & 0 \end{bmatrix} where ##a\in\mathbb{R}^+##. The initial state of the system...
  21. D

    A Expectation values and trace over the environment

    I've worked through a Stern Gerlach experiment for the Sx and Sz directions using the density matrix formalism to account for the environment. This shows a result which I think is correct but relies on decoherence to give the "actual" value. I'm not confident about the result though. Would...
  22. J

    I Free Particle: Time dependence of expectation values Paradox

    It would be really appreciated if somebody could clarify something for me: I know that stationary states are states of definite energy. But are all states of definite energy also stationary state? This question occurred to me when I considered the free particle(plane wave, not a Gaussian...
  23. J

    I Expectation value of momentum for free particle

    Hello! Could somebody please tell me how i can compute the expectation value of the momentum in the case of a free particle(monochromatic wave)? When i take the integral, i get infinity, but i have seen somewhere that we know how much the particle's velocity is, so i thought that we can get it...
  24. bananabandana

    Time Evolution of Operators

    Homework Statement [/B] For a general operator ## \hat{O}##, let ##\hat{O}_{mn}(t)## be defined as: $$ \hat{O_{mn}}(t) = \int u^{*}_{m}(x,t) \hat{O} u_{n}(x,t) $$ and $$ \hat{O_{mn}} = \int u^{*}_{m}(x) \hat{O} u_{n}(x) $$ ##u_{m}## and ##u_{n}## are energy eigenstates with corresponding...
  25. entropy1

    I Expectation value in terms of density matrix

    It says in Susskind's TM: ##\langle L \rangle = Tr \; \rho L = \sum_{a,a'}L_{a',a} \rho_{a,a'}## with ##a## the index of a basisvector, ##L## an observable and ##\rho## a density matrix. Is this correct? What about the trace in the third part of this equation?
  26. M

    Expectation value and momentum for an infinite square well

    Homework Statement √[/B] A particle in an infinite square well has the initial wave function: Ψ(x, 0) = A x ( a - x ) a) Normalize Ψ(x, 0) b) Compute <x>, <p>, and <H> at t = 0. (Note: you cannot get <p> by differentiating <x> because you only know <x> at one instance of time)Homework...
  27. Q

    Expectation Value- Mean Time to Failure

    Homework Statement (a) Suppose we flip a fair coin until two Tails in a row come up. What is the expected number, NTT, of flips we perform? Hint: Let D be the tree diagram for this process. Explain why D = H · D + T · (H · D + T). Use the Law of Total Expectation (b) Suppose we flip a fair...
  28. S

    I Difference between expectation value and eigenvalue

    There is another topic for this but I didn't quite see it and I don't know how I've gone so far through my course not asking this simple question. So what's the difference? My thought process for hydrogen. I know it can have quantised values of energy, the energy values are the Eigen values of...
  29. J

    A Higgs Expectation Value with Classical vs Quantum Potential

    I'm having a hard time following the arguments of how the Higgs gives mass in the Standard Model. In particular, the textbook by Srednicki gives the Higgs potential as: $$V(\phi)=\frac{\lambda}{4}(\phi^\dagger \phi-\frac{1}{2}\nu^2)^2 $$ and states that because of this, $$\langle 0 | \phi(x)...
  30. B

    Expectation Value of Hamiltonian with Superposition

    Homework Statement [/B] Particle in one dimensional box, with potential ##V(x) = 0 , 0 \leq x \leq L## and infinity outside. ##\psi (x,t) = \frac{1}{\sqrt{8}} (\sqrt{5} \psi_1 (x,t) + i \sqrt{3} \psi_3 (x,t))## Calculate the expectation value of the Hamilton operator ##\hat{H}## . Compare it...
  31. G

    Harmonic oscillator positive position expectation value?

    So this is something that troubled me a bit- in Shankar's PQM, there's an exercise that asks you to find the position expectation value for the harmonic oscillator in a state \psi such that \psi=\frac{1}{\sqrt{2}}(|0\rangle+|1\rangle) Where |n\rangle is the n^{th} energy eigenstate of...
  32. F

    MHB Calculating Expectation of $X$ for a Nonnegative RV

    Good morning. Can you help me to solve this exercise. The correct answer should be the 2, but how is it calculated? Thanks. Let $l_{+}$ be the set of nonnegative simple rv’s. Pick $X=7\cdot I _{\left \{ X\leqslant 7 \right \}}+7\varepsilon \cdot I_{\left \{ X> 7 \right \}}\epsilon l_{+}$ , for...
  33. phys-student

    Finding expectation values for given operators

    Homework Statement The Hamiltonian of an electron in solids is given by H. We know that H is an Hermitian operator, it satisfies the following eigenvalue equation: H|Φn> = εn|Φn> Let us define the following operators in terms of H as: U = e^[(iHt)/ħ] , S = sin[(Ht)/ħ] , G = (ε -...
  34. T

    Calculating expectation value of U

    Homework Statement ## H ## is the Hamiltonian of an electron and is a Hermitian operator. It satisfies the following equation: ##H |\phi_n\rangle = E_n |\phi_n\rangle ## Let ## U = e^{\frac {iHt}{\hbar}} ##. Find the expectation value of U in state ##|\phi_n\rangle## Homework Equations ##...
  35. edguy99

    Adding expectation values to a CHSH animation

    An animation of the CHSH experiment to generate correlated photons is at: http://www.animatedphysics.com/games/photon_longdistance_chsh.htm @georgir has a program to show the calculations using the formula for photon detection return Math.random() < (Math.cos(r(p-a)*2)+1)/2; yields the...
  36. B

    About the expectation value of position of a particle

    I am following Griffiths' intro to quantum mechanics and struggling(already) on page 16. When a particle is in state ##\Psi##, $$\frac{d<x>}{dt} = \frac{i\hbar}{2m}\int_{-\infty}^{\infty} x\frac{\partial}{\partial t}\bigg (\Psi^*\frac{\partial \Psi}{\partial x}-\frac{\partial \Psi^*}{\partial...
  37. Clarky48

    Dirac notation - expectation value of kinetic energy

    It's my first post so big thanks in advance :) 1. Homework Statement So the question states "By interpreting <pxΨ|pxΨ> in terms of an integral over x, express <Ekin> in terms of an integral involving |∂Ψ/∂x|. Confirm explicitly that your answer cannot be negative in value." ##The 'px's should...
  38. M

    Why Does ½ Factor in HF Expectation Value?

    I am not sure why a factor of (½) appears in front of the summation over orbitals, i, j to N, of the Coulomb and exchange integrals in the HF energy expectation value.
  39. H

    Why Do Single Source Diagrams Matter in Vacuum Expectation Value Calculations?

    Srednicki page 65 it says "Let us compute the vacuum expectation value of the field $$\phi(x)$$ which is given by $$\langle 0| \phi (x)|0 \rangle = \frac{\delta}{\delta J(x)} Z_{1}(J) |_{J=0}$$ This expression is then the sum of all diagrams that have a single source, with the source removed."...
  40. M

    Expectation of position and momentum at time t, pictures

    Homework Statement Consider a particle, with mass m, charge q, moving in a uniform e-field with magnitude E and direction X_1. The Hamiltonian is (where X, P, and X_1 are operators): The initial expectation of position and momentum are <X(0)> = 0 and <P(0)>=0 Calculate the expectation...
  41. D

    Expectation value of spin 1/2 particles along different axes

    Homework Statement Show that for a two spin 1/2 particle system, the expectation value is \langle S_{z1} S_{n2} \rangle = -\frac{\hbar^2}{4}\cos \theta when the system is prepared to be in the singlet state...
  42. W

    Cantelli's Inequality and Chebyshev's Inequality

    Homework Statement The number of customers visiting a store during a day is a random variable with mean EX=100and variance Var(X)=225. Using Chebyshev's inequality, find an upper bound for having more than 120 or less than 80customers in a day. That is, find an upper bound on P(X≤80 or X≥120)...
  43. W

    Markov's Inequality for Geometric Distribution.

    Homework Statement Let X∼Geometric(p). Using Markov's inequality find an upper bound for P(X≥a), for a positive integer a. Compare the upper bound with the real value of P(X≥a). Then, using Chebyshev's inequality, find an upper bound for P(|X - EX| ≥ b). Homework Equations P(X≥a) ≤ Ex / a...
  44. W

    Conditional Expectation of Multiple Independent Random Varia

    Homework Statement Given X,Y,Z are 3 N(1,1) random variables, (1) Find E[ XY | Y + Z = 1] Homework EquationsThe Attempt at a Solution I'm honestly completely lost in statistics... I didn't quite grasp the intuitive aspect of expectation because my professor lives in the numbers side and...
  45. N

    How can expectation of position^2 be > L

    How can position^2 expectation be greater than the Length of "box"? I mean <x^2> = L^2 / 3. Say L=100m then we have <x^2> = 333m. How is this possible?
  46. M

    Expectation value of observable in Bell State

    Homework Statement Consider the bipartite observable O_AB = (sigma_A · n) ⊗ (sigma_B · m) Where n and m are three vectors and sigma_i = (sigma_1_i, sigma_2_i, sigma_3_i) with i = [A,B] are the Pauli vectors. Compute using abstract and matrix representation the expectation value of O_AB...
  47. J

    Solving Gaussian Random Variable Expected Value: CDF & Expectation

    Hi, I have trouble with the following problem: Gaussian random variable is defined as follows \phi(t) = P(G \leq t)= 1/\sqrt{2\pi} \int^{t}_{-\infty} exp(-x^2/2)dx. Calculate the expected value E(exp(G^2\lambda/2)). Hint: Because \phi is a cumulative distribution function, \phi(+\infty) =...
  48. J

    E[(X^2+Y^2)/XY] for Geometric(p) R.V.s

    The Question Let X and Y be two independent Geometric(p) random variables. Find E[(X^2+Y^2)/XY]. Formulas Px(k) = py(k) = pq^(k-1) E(x) = Σx(p(x)) My attempt at a solution I am really struggling with this question because I want to apply the LOTUS equation but am unsure how to do it for...
  49. C

    Making use of completion relation to find general expectation

    I am stuck on this Self-test 1.6 in molecular quantum mechanics by atkins and friedman. Probably making use of the completeness relation the question is the following: Show that if <Ωf>*=-Ωf*, then <Ω>=0 for any real function f. Anyone got a clue?
  50. T

    Calculating Expectation Values for Independent Random Variables

    Homework Statement If X1 has mean -3 and variance 2 while X2 has mean 5 and variance 4 and the two are independent find a) E(X1 - X2) b) Var(X1 - X2)The Attempt at a Solution I am not very clear on what I am supposed to be doing for this problem. I don't fully understand this expectation value...
Back
Top