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.
Homework Statement
Let Bt be a standard Brownian motion. Let s<t:
a) Compute P(\sigma B_{t}+\mu t|B_{s}=c)
b) Compute E(B_{t}-t|B_{s}=c)
Homework Equations
Defition of brownian motion: B(t) is a (one-dim) brownian motion with variance \sigma^{2}if it satisfies the following conditions:
(a)...
Every quantum mechanical operator has an observable in classical mechanics
<x> - position
...
<x^2> - ?
<p^2> - ?
What is the meaning on these expectation values?
v^2 = <x^2> - <x>^2
What is the meaning of this? edit: It looks to me like uncertainty in position. Is it the average...
fx,y = 6(x-y)dydx, if 0<y<x<1
how do you find E(XY),
i know the formula...g(x,y)fxy(x,y)dydx
but i don't know what 'g(x,y)' represents and the limits to use??
Homework Statement
The variance of an observable Qhat in a state with wavefunction psi is,
(delta Qhat)2=<(Qhat-<Qhat>)2>
Show that this can be written as,
(delta Qhat)2=<Qhat2>-<Qhat>2
Homework Equations
As above.
The Attempt at a Solution
(delta...
Homework Statement
calculate <x>, when \Psi(x,t)=A*exp(-(\sqrt{}Cm/2h)x^{}2
Homework Equations
<x>=\int\Psi^{}*x\Psidx over all space..
\intexp(-\alphax^{}2)=\sqrt{}\pi/\alpha
The Attempt at a Solution
ok know how to do this but how do i do the intergral... my maths isn't so good...
http://img23.imageshack.us/img23/1649/93412460.th.png
For question 2 in the above link,
I calculated the expectation of the energy by
E=<\hat{H}>=\int_0^a \psi^* \hat{H} \psi dx
where \psi=\psi^*=x(a-x)
this gave E=0. this answer confused me for two reasons:
(i) is it ok for the...
Homework Statement
http://209.85.48.12/3560/8/upload/p2791776.jpg
Homework Equations
The most relevant identity to the part that I'm confused about is the following identity: for any cumulative distribution function F, with the inverse function F-1, if U has uniform (0,1) distribution...
Hi all.
I have a question which arose from the answer of a homework problem. A particle is in the state given by
\left| \psi \right\rangle = \frac{1}{{\sqrt 3 }}\left[ {\left| \psi \right\rangle _1 + \left| \psi \right\rangle _2 + \left| \psi \right\rangle _3 } \right],
where {\left|...
Hi quick question:
Suppose you have a function of random variables given in the following way
Z=X if condition A
Z=Y if condition B
where both X and Y are random variables, and conditions A & B are disjoint.
Then would the expectation of Z be
E[Z]=E[X]*Pr(A)+E[Y]*Pr(B)?
Thanks in advance.
Homework Statement
Let X and Y be contnious random variables with joint probability density function -
f(x,y) = 10x^2y if 0<x<y<1 0 othewise
a) Determine P( Y < \frac{X}{2})
b) Determine P(x \leq 1/2 | Y < X^2)
c) Determine the marginal density functions of X and Y, respectively...
This result isn't in our book, but it is in my notes and I want to make sure it's correct. Please verify if you can.
Homework Statement
I have two I.I.D random variables. I want the conditional expectation of Y given Y is less than some other independent random variable Z.
E(Y \...
If W=g(X) is a function of continuous random variable X, then E(W)=E[g(X)]=
∞
∫g(x) [fX(x)] dx
-∞
============================
Even though X is continuous, g(X) might not be continuous.
If W happens to be a discrete random variable, does the above still hold? Do we still integrate ∫...
Is the expectation value of momentum/position/energy the value that we're most likely to measure? So suppose we measure 100 particles with the same wavefunction, would we expect most of them to have momentum/position/energy that's equal to the expectation value? And I was wondering, how do we...
Homework Statement
prove or disprove that E[X^2] = E(X)^2
Homework Equations
E[X] = \sumxi*pr(xi)
The Attempt at a Solution
I really don't know where to start, I believe that it is not true, so I should try to disprove it, and the easiest way to do that would be by...
Thanks for all the help on the first question but now I have to solve for <T>. I have no idea how to do this, and I could use some help for a kick start. thanks!
first post! but for bad reasons lol
Im trying to find <x> and <p> for the nth stationary state of the harmonic potential: V(x)=(1/2)mw^2x^2
i solved for x: x=sqrt(h/2mw)((a+)+(a-))
so <x> integral of si x ((a+)+(a-)) x si.
therefor the integral of si(n+1) x si + si(n-1) x si.
si(n+1)...
Homework Statement
Consider a wave function \psi (x,t) = R(x,t) exp(i S(x,t)) what is the expectation value of momentum?Homework Equations
<f(x)> = \int^{\infty}_{-\infty} \psi^* f(x) \psi dx
\hat{p} = -i \hbar \frac{\partial}{\partial x} The Attempt at a Solution
This is for an intro to...
Homework Statement
The expectation value <r> of the electron-nucleus separation distance 'r' is:
<r> = ʃ r |ψ|² dV.
(a) Determine <r> for the 1, 0, 0 state of hydrogen.
The Attempt at a Solution
Right, I've obtained the value for ψ = (1/πa³)^1/2 exp(-r/a)
I then...
Homework Statement
I have to prove the following:
\hbar \frac{d}{dt}\langle L\rangle = \langle N \rangle
Edit: L = Angular Momentum & N = Torque
Homework Equations
I used Ehrenfest's theorem, and I've got the equation in the following form:
\frac{1}{i} \left(\left[L,H\right]\right) +...
Homework Statement
I need to find the expectation value for E but I don't know how b acts on the vacuum state.
Homework Equations
b = \int dt \phi^{*}(t) \hat{{\cal E}}_{in}(t)
| \psi(t)\rangle = b^\dagger| 0\rangle
The Attempt at a Solution
\langle \psi(t) |...
Homework Statement
I we know the eigenstates of the system be |\psi_1\rangle and |\psi_2\rangle. Current state of the system is
|\Psi\rangle = c_1 |\psi_1\rangle + c_2 |\psi_2\rangle
Try to find the expectation value of electric dipole moment \mu (assume it is real) and write it in...
Homework Statement
Obtain an expression for the expectation value <Pxn>n N=1,2... of a particle in an infinite box ( V=\infty for x<0 and x>L ; V=0 for 0<X<L) which is in an eigenstate of the energy.
Homework Equations
Pn =+- \sqrt{2*m*En } = +- (n*pi*Hbar) / L
The Attempt at a...
Homework Statement
Hi all,
i have a problem:
i am given a time-dependent wavefunction, Ψ(x,t), and i am asked to calculate the expectation value of total energy E(t) and potential energy V(t).
Ψ(x,t) = (1/sqrt2)[Ψ0(x).e-[i(E0)t/h] + Ψ1(x)e-[i(E1)t/h]],
where Ψ0,1(x) are the ground and...
Homework Statement
For a given wave function Psi(x,t)=Aexp^-(x/a)^2*exp^-iwt*sin(kx) find the expectation value of the linear momentum.
Homework Equations
<p>=integral(-inf,inf) psi* p^ psi dx
p^=-ih(bar) d/dx
sin x = (exp ix - exp -ix)/2i
cos x = (exp ix + exp -ix)/2
The Attempt...
Quantum homework - Average Expectation Values??
Hi people,
I'm struggling with my quantum mechanics homework - I've included links to photographs of my attempts at solutions, but i know they are wrong because I am given what the answers are supposed to be. Can somebody help me spot where I am...
Homework Statement
Calculate \Delta x = \sqrt{\left\langle(x - \left\langle x \right\rangle )^2 \right\rangle} if \left\langle x \right\rangle = 0 and \left\langle x^2 \right\rangle = a^2(\frac{\pi - 6}{12 \pi^2})
2. The attempt at a solution
\left\langle(x - \left\langle x...
I seem to be having a rather difficult time understand all the details of the notation used in this quantum material. If I'm given the eigenvalue equations for L^{2} and L_z and L_{\stackrel{+}{-}} for the state |\ell,m>, how do I compute <L_{x}> using bra-ket formalism? I know that L_x =...
Homework Statement
A particle is in a infinite square poteltian well between x=0 and x=a. Find <p> of a particle whose wave function is \psi(x) = \sqrt{\frac{2}{a}}sin\frac{n \pi x}{a} (the ground state).
2. The attempt at a solution
<p> = \frac{2 \hbar k}{\pi} \int^{a}_{0}sin^{2}...
Hi,
You know famous equation, \frac{d<A>}{dt} = <\frac{i}{\hbar}[\hat{H},\hat{A}] + \frac{\partial\hat{H}}{\partial t} >
But liboff said if \frac{\partial \hat{A} }{\partial t} = 0 then, \frac{d<\hat{A}>}{dt} = 0
this is the proof
\frac{d<A>}{dt} =...
the number of hairs Nsub.1 on a certain rare species can only be the number 2sup.l(l=0,1,2...) The probability of finding such an animal with 2sup.l hairs is exp-1/l ! what is the expectation,<N>? what is deltaN?
Let X and Y be two random variables.
Say, for example, they have the following joint probability mass function
x
-1 0 1
-1 0 1/4 0
y 0 1/4 0 1/4
1 0 1/4 0
What is the proper way of computing E(XY)?
Can I let Z=XY and find E(Z)=∑...
Homework Statement
Here is another True or False question from the same practice test.
Since the expectation of the momentum operator <p>=<n|pn> is zero for an energy eigen state of the harmonic oscillator, a measurement of the momentum will give zero every time (True or False)...
I need help about conditional expectation for my research. I get stucked on this point. Could anyone show me how to prove that:
"Let E[|Y|]<∞. By checking that Definition is satisfied, show that if Y is measurable F0, then E[Y|F0]=Y."
Def: Let Y be a random variable defined on an underlying...
Homework Statement
Hi all.
The expectation value for S_x (spin in x-direction) is:
\left\langle {S_x } \right\rangle = \left\langle {\phi |S_x \phi } \right\rangle = \phi ^\dag S_x \phi
where \phi is the state and \phi^"sword" is the hermite conjugate.
My question is: I...
Homework Statement
A cell diverges into X new cells. Each of them reproduces in the same manner. X is a geometric random variable with success parameter of 0.25.
What is the expectation of the number of great-grandsons a cell have?
2. The attempt at a solution
I thought about using the...
I am having some great difficulty getting intuition out of the standard quantization of the Klein-Gordon Lagrangian.
consider the H operator. In QM, the expectation values for H in any eigenstates |n> is just
<n|H|n>
now, in QFT, suppose I have a state |p> in the universe, what do I get if I...
Homework Statement
I need to find the expectation value of x of an aharmonic oscillator of a given potential:
V_{(x)} = c x^2 - g x^3 - f x^4
Homework Equations
Two relevant equations:
First:
I'm using the partition function to find the expectation value
<x>= \frac { \int x Z...
Homework Statement
First off, this is my first time posting here so please excuse any editing mistakes or guidelines I may have overlooked.
This is problem 1.17(c) from Griffiths, Introduction to Quantum Mechanics 2nd edition. It reads: \Psi(x, 0) = A(a^2 - x^2), -a\leqx\leqa. \Psi(x, 0)...
Homework Statement
Hi all.
Let's say that i have a wave function
\Psi (x,t) = A \cdot \exp ( - \lambda \cdot \left| x \right|) \cdot \exp ( - i\omega t)
I want to find the expectation value for x. For this I use
\left\langle x \right\rangle = \int_{ - \infty }^\infty x \left| \Psi...
Problem
Consider an operator \hat{A} whose commutator with the Hamiltonian \hat{H} is the constant c... ie [\hat{H}, \hat{A}] = c. Find \langle A \rangle at t > 0, given that the system is in a normalized eigenstate of \hat{A} at t=0, corresponding to the eigenvalue a.
Attempt Solution
We...
On pages 16-17 of Griffith's Intro to QM, he writes the following:
\frac{d\left\langle x \right\rangle}{dt}= \int x \frac{\partial}{\partial t}|\Psi|^{2} dx = \frac{i\hbar}{2m}\int x \frac{\partial}{\partial x} \left( \Psi^{*}\frac{\partial\Psi}{\partial x}- \frac{\partial\Psi^{*}}{\partial...
The state \Psi = \frac{1}{\sqrt{6}}\Psi-1 + \frac{1}{\sqrt{2}}\Psi1 + \frac{1}{\sqrt{3}}\Psi2
is a linear combination of three orthonormal
eigenstates of the operator Ô corresponding
to eigenvalues -1, 1, and 2. What is the
expectation value of Ô for this state?
(A) 2/3
(B)...
I need some help with "law of total expectation".
Sorry for my English, I don't know the right English expressions.
The Problem is:
People come (show in) with with Poisson rate of 10 people per hour.
There is a 0.2 chance that a person will give money to a beggar sitting in the corner.
The...
We all know the concept of expectation value,it is the average of all possible outcomes of an experiment. Mathematically average of x is written as (Σnkxk / Σnk ). Quantum-mechanically nk is represented by probability density(P), where P = ∫Ψ*Ψ d3r,
then <r> = ∫ r P(r) d3r -----------(1)...
I am quite new to Quantum Mechanics and I am studying it from the book by Griffiths, as kind of a self-study..no instructor and all...
For a gaussian wavefunction \Psi=Aexp(-x^{2}), I calculated
<p^{2}> and found it to be equal to ah^{2}/(1-2aiht/m)
(By h I mean h-bar..not so good at...
i'm just not sure on this little detail, and its keeping me from finishing this problem.
take the arbitrary operator \tilde{p}^{n}\tilde{y}^{m} where p is the momentum operator , and x is the x position operator
the expectation value is then <\tilde{p}^{n}\tilde{y}^{m} >
is this the same...
can anyone give me any ideas on how to evaluate this:
<z>=<\Phi1|z|\Phi2>
(for say hydrogen wavefunctions). Similarly
<x+iy>=<\Phi1|x+iy|\Phi2>
FYI, I'm trying to understand how radiation is polarised (an external B field polarises radiation, so we must consider the dipole...