Value Definition and 1000 Threads

Hi everyone, I do experiment in field of quantum optics and I want to calculate the mean of the number of photons (MNP). In the most of papers, MNP can be calculated by using average power which is measured by power meter. But my power meter is defective. For now, I have only the avalanche...

Homework Statement There are two possible solutions for 'a' for which ##f(x)=|x^x-x^a|## is a probability density function. Determine the value for a which produces a PDF with the largest probability of random variable 'x' falling within two standard deviations either side of the mean.Homework...

Hello all, I have a few small questions regarding logarithms, which I would like to ask your help with. 1) A car loses 50% of it's value every 4 years. How many years does it take for the car to lose 1/3 of it's value ? (I think you need log with basis of 2 here, but not sure) 2) A company...

Does anyone know how can you prove that the mean value of the tensor operator S12 in all directions r is zero? S12 : http://prntscr.com/j3gn40 where s1, s2 are the spin operators of two nucleons.

Homework Statement i have no idea how to proceed

Homework Statement Homework Equations ##ΔV=Ed## The Attempt at a Solution ##V_A=E l## ##V_b=0## , because point B is perpendicular to the electric field ##ΔV = V_a + V_b## = El Is my answer correct ?

Hey! :o The geometric distribution with parameter $p\in (0,1)$ has the probability function \begin{equation*}f_X(x)=p(1-p)^{x-1}, \ \ x=1, 2, 3, \ldots\end{equation*} I have shown that $f_X$ for each value of $p\in (0,1)$ is strictly monotone decreasing, as follows...

Hello everyone, I would be happy if someone explained the small reduced chi squared value to me. I have fitted a set of measured data with an exponential function, which I need for some sw calculations. The fit seams great, the origin sw also provides the reduced chi squared, but it is very...

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...

This question comes from the "Introduction to Probability" book (Blitzstein & Hwang). Martin has just heard about a gambling strategy: bet 1 dollar that a fair coin will land heads. If it does, stop. If it lands tails, then double the bet for the next toss, now betting 2 dollars on heads. If it...

Homework Statement y(w)= 3/(iw-1)^2(-4+iw) Homework Equations N/A The Attempt at a Solution 3/(iw-1)^2(-4+iw) = A/iw-1 + B/(iw-1)^2 + C/-4+iw for B iw = 1 B=3/-4+1 = -1 for C iw = 4 C= 3/(4-1)^2 = 1/3 I know the answer for A should be -1/3 however I am unsure how to obtain this as if the...

Homework Statement Given that vector a = (1, 2, -5), b = (-12, 41, 75) and c = a + 2b, explain why (without doing any calculations whatsoever) the value of a•(b x c) = 0 Homework Equations No specific equations, as the question asks for the value without making any calculations. This problem...

Homework Statement Homework EquationsThe Attempt at a Solution [/B] I got the first 2 parts, but I'm having trouble with the last one. For the time the switch S1 is closed, I derived ##q(t) = CE(1 - \cos(\frac{t}{\sqrt{LC}}))##, by writing the loop equation ##\frac{E}{L} - \frac{1}{LC}q =...

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...

On Griffiths's book page 166 first paragraph he said " It's not merely that you don't know all three components of L; there simply aren't three components—a particle just cannot have a determinate angular momentum vector, any more than it can simultaneously have a determinate position and...

Given an ##N## dimensional binary vector ##\mathbf{v}## whose conversion to decimal is equal to ##j##, is there a way to linearly map the vector ##\mathbf{v}## to an ##{2^N}## dimensional binary vector ##\mathbf{e}## whose ##(j+1)##-th element is equal to ##1## (assuming the index starts...

Rule: Suppose a>0, then |x|>a if and only if x>a OR x<-a So |x|>|x-1| becomes: x>x-1 which is false (edit: or more accurately doesn't give the whole picture, it implies true for all x) OR x<-x+1 2x<1 x<1/2 which is false

Homework Statement I have taken 5 sets of readings of voltage against angle for an experiment to determine specific rotation. (I'm using the maxima to determine the phase shift) So, having averaged these values and determined the maximum, I can then trace back to the angle at which this...

I am working on Value at Risk and expected shortfall/conditional Value at Risk.The formula I have is this: What I do not understand is numerator of the second part. If for example I want to look at an expected shortfall when p=0.01 (ignoring the average and the standard deviation). what value...

How do I determine which trig value is bigger or smaller without using a calculator? Sample: Which is bigger: cos 2 or sin 2?

Homework Statement I'm determining g by the extension of a spring. I used a PASCO motion sensor to record the displacement of the spring towards the sensor since it is more accurate than myself using a ruler. The uncertainty in the distance on the sensor is 0.8%. I get the uncertainty in...

Hypothetical question: Let's say there's a granite cube with a volume of 60 cubic centimeters. A cannon ball is shot at it, reducing it to rubble, and the kinetic energy of the ball was 10,000 joules. We use the same ball with the same kinetic energy output on a stronger unknown substance with...

Homework Statement Find the exact value of ##y=cos\left(arcsin \frac {5} {11} \right)## Homework EquationsThe Attempt at a Solution I'm stuck at square one. I know that I must evaluate arcsin first, which will give me an angle θ. From that angle, I can take the cosine of it and that much makes...

Homework Statement Suppose we have the standard rectangular potential barrier in 1D, with $$ V = \left\{ \! \begin{aligned} 0 & \,\text{ if } x<0, x>d\\ V_0 & \,\text{ if } x>0,x<d\\ \end{aligned} \right. $$ The standard approach to solve for tunneling through the barrier is to match the...

The problem I'd like to calculate the value of this sum: $$3 \sum^\infty_{k=1}\frac{1}{2k^2-k}$$The attempt ## 3 \sum^\infty_{k=1}\frac{1}{2k^2-k} = [k=t/2] = 3 \sum^\infty_{t=2}\frac{1}{2 \left( \frac{t}{2} \right)^2-\frac{t}{2}} = 3 \sum^\infty_{t=2}\frac{1}{ \frac{t^2}{2} - \frac{t}{2}} = 3...

Explain, in your own words, why there are no real numbers that satisfy the absolute value equation | x^2 + 4x | = - 12. Can we say there is no real number solution here? If so, is the answer then imaginary taught in some advanced math class?

Homework Statement Homework Equations ## y(t)\mu(t) - y(t_0) \mu(t_0) = \int_{t_0}^t \mu(s) g(s) ds## ## y(t) = \frac{1}{\mu(t)} \left[y_0 \mu(t_0) + \int_{t_0}^t \mu(s)g(s) ds\right]## The Attempt at a Solution (7 lines)I have done the first part, which seems correct, yet I am stuck with...

Homework Statement The problem is to calculate the baud rate of a serial transmission by measuring the length of time required to send the ASCII character 'Z' over a serial port. The serial port settings are 9600 baud with a start and stop bit, no parity and a data size of 8 bits. Homework...

Hello, How does one go about algebraically checking if |x+|y+z|| and ||x+y|+z| are equal?

Homework Statement Hi I'm having a trouble with finding min value of given function: f(x) = sqrt((1+x)/(1-x)) using derivative.First derivative has no solutions and it is < 0 for {-1 < x < 1} when f(x) is given for {-1 < x <= 1}. For x = - 1 there is a vertical asymptote and f(x) goes to +...

Determine the value of n if 1 + 3 + 6 + ... + $$\frac{1}{2}$$n(n - 1) = 364 What I did: I know that 1, 3, and 6 are the result of arithmetic series with the starting value 1 and the difference 2, thus that sum can be written as S1 + S2 + S3 + ... + Sn = 364. However, by assuming that Sn =...

Homework Statement We release a ball from a height h and it bounces for a time t. What is the value of k (the quotient of the ball's momentum before and after collision with the ground)? Homework EquationsThe Attempt at a Solution I'm kind of lost here. :/ [/B]

https://imgur.com/a/Maq1N 1. Homework Statement Attached above is the problem statement. Essentially, they've given two different volumes involving some unknown function f(x) and ask that you find its average value over the given closed interval. Homework Equations Relevant equations include...

Homework Statement In triangle ABC AC= 9cm, BC=5cm and angle ACB = β in degrees. Given that cos2β=0.84, determine (i) the exact value of sin2B (ii) the value of β if 90°<β<180° (iii) the length of AB Homework Equations sin2θ+cos2θ=1 The Attempt at a Solution Using that equation In relevant...

Homework Statement Consider a continuous random variable X with the probability density function fX(x) = |x|/5 , – 1 ≤ x ≤ 3, zero elsewhere. I need to find the cumulative distribution function of X, FX (x). 2. Homework Equations The equation to find the cdf. The Attempt at a Solution FX(x)...

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|...

Homework Statement Given f(x)=\frac{3x-2}{x+1} Calculate the value of x, for which f(x) is undefined. Homework EquationsThe Attempt at a Solution Hi, I've never come across this before and I'm not finding anything on the internet, I would post my attempt but the problem is I don't know where...

Homework Statement Hello, I have three matrices A = [3 -4 2 1] B = [α β] C= [α 5] The question now states AB = C Find the values of (alpha) and (beta). Homework EquationsThe Attempt at a Solution I found the inverse of A, then I multiplied each side of the equation AB=C by the inverse...

Homework Statement For AC Circuit shown in the picture, ##C=60nF##, ##L=100uH##, ##X_3=-100Ω##, ##Z_2=50Ω## and ##Φ_2=\frac {\pi}{6}##. When the switch is closed the ammeter shows a current ##I_1=0.6A## and the voltmeter shows ##U_l=60V##. The measuring instruments mentioned are ideal...

Homework Statement [/B]Homework Equations I used voltage divider rule. The Attempt at a Solution I get value of a = 3 Book answer is 1.5. Is book wrong or am I wrong?

Hi, it may be interesting question but what is the d (dy)/dx (y is function of x)? I think it is nearly zero but if it is 0 then how can we prove it?

Hello all, Given the following matrix, \[A=\begin{pmatrix} 2 & 6\\ 1 & a \end{pmatrix}\] and given that \[\lambda =0\] is an eigenvalue of A, I am trying to determine that value of a. What I did, is to create the characteristic polynomial \[(\lambda -2)*(\lambda -a)+6=0\] and given...

Hi, I was wondering what is the physical meaning of these integrals: \begin{equation} \int_{-\infty}^{\infty} \psi \psi^* dx = 0 \end{equation}\begin{equation} \int_{-\infty}^{\infty} \psi x \psi^* dx = 0 \end{equation} \begin{equation} \int_{-\infty}^{\infty} \psi p \psi^* dx = NA...

I'm trying to extract the expected value of a |+45> polarized photon in the HV- base. I do it in two ways, one is correct and the other I get wrong answer. What am I doing wrong in the first method that is wrong? method 1 method 2 thanks in advance

We obtain equations of motion by solving the Euler-Lagrange equations; along this path the action ##S## is an extremum. We are usually interested in the path ##x(t)## (in one dimension) connecting ##x(0)=x_0## and ##x(T)=x_1##. But does the numerical (extremal) value of the resulting action have...

What is the value of "delayed choice" experiments? Disclaimer: I do realize that nearly any experiment deserves to be performed even to make sure the QM theory predicts the results of such experiment right. So I have no objections to the work of people which implemented these sorts of...

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...

This is rather basic, and may be a misconception of the notation, however, I can't make the following sum up: The following is given: x_n(t) = 1 -nt , (if 0 <= t <= 1/n) and 0, (if 1/n < t <= 1) However, this part I can't grasp this part in the book: \begin{equation} ||x_n||^2 = \int_0^1...

Hi, I have another question, if A and B are mxn matrices, how do I prove that $AA^T = BB^T$ iff $A = BO$ where $O$ is some orthogonal matrix? I think I need to use a singular value decomposition but I am not sure. Thanks!

Hi Friends, I have x gross amount a = 1739598, Rate of interest R = 5%, and day difference d = 1. Future cash flow f = 176100 now npv = f/(1+r)^(d/360) i.e. 176100/(1+0.05)^(1/360) = 176076.135095 PA = a - npv i.e. 1739598 - 176076.135095 = 1563521.8649 round off value 1563522 rate CR =...