Value Definition and 1000 Threads

I know that the eigenstates of momentum operator are given by exp(ikx) To construct a real-valued and normalized wavefunction out of these eigenstates, I have, psi(x) = [exp(ikx) + exp(-ikx)]/ sqrt(2) But my trouble is, how do I find the expectation value of momentum operator <p> using this...

But I think the answer is 32, is it correct?

Hi folks, a question regarding the value of G, has there been an experimental data collected on the value of G over time, what I'm interested in, is if the value of G in the observable universe, is decreasing or increasing (by a small amount) over time, thanks.

Hey! :giggle: Let $X$, $Y$ and $Z$ be independent random variables. Let $X$ be Bernoulli distributed on $\{0,1\}$ with success parameter $p_0$ and let $Y$ be Poisson distributed with parameter $\lambda$ and let $Z$ be Poisson distributed with parameter $\mu$. (a) Calculate the distribution...

The expectation value of the kinetic energy operator in the ground state ##\psi_0## is given by $$<\psi_0|\frac{\hat{p^2}}{2m}|\psi_0>$$ $$=<\psi_0|\frac{1}{2m}\Big(-i\sqrt{\frac{\hbar mw}{2}}(\hat{a}-\hat{a^{\dagger}})\Big)^2|\psi_0>$$ $$=\frac{-\hbar...

There are 8 items in a data set. The sum of the items is 48. a. Find the mean. $\qquad\textit{mean}=\dfrac{\textit{sum}}{\textit{data set}}=\dfrac{48}{8}=\textbf{6}$ The variance of this data set is 2. Each value in the set is multiplied by 3. b. Write down the value of the new mean. $\qquad...

Hey! :giggle: Let $f(x)=e^{-x}\sin (x)$, $x\in \mathbb{R}$. a) Calculate the Taylor polynomial of order $4$ at $0$. b) Calculate the value of $f \left (\frac{1}{2}\right )$ using estimation for the remainder with an error not more than $\frac{1}{400}$.I have done question a) ...

When I run this simple code: int main() { int x = 45; std::unique_ptr<int> q(new int (x)); *q = 3; cout << x << endl; } 45 is printed on the console. I expected this to print 3 to the console. It prints 3 when I use a built-in pointer. Does this mean that unique pointer...

I replace b with any value greater than 0 and then solve for c. Right?

A recent thread by @coolcantalope was accidentally deleted by a Mentor (I won't say which one...), so to restore it we had to use the cached version from Yahoo.com. Below are the posts and replies from that thread. The cached 2-page thread can be found by searching on the thread title, and is...

Here is my attempt at a solution I don’t know where to go from here, as the equation is a quadratic it will have two solutions which means there will be two stationary points, but I don’t know how to solve for z.

Hi, I'm currently a Grade 11 student and I need help for this question (Precalculus): If $\sum\limits_{i=1}^{50} f(i)=90$ and $\sum\limits_{i=30}^{50} g(i)=60$, what is the value of $\sum\limits_{i=1}^{50} (7 g(i)-f(i)+12)/(2)$? P.S. To those who could answer this, it would be a great help...

I was trying this problem from some 2 hours but unable to crack it. I cannot proceed after few lines i.e$${\frac{axsin\theta}{cos^2\theta}} - {\frac{bycos\theta}{sin^2\theta}} = 0$$ $${\frac{axsin\theta}{cos^2\theta}} = {\frac{bycos\theta}{sin^2\theta}}$$ $${\frac{ax}{by}}...

First thank you for taking your time to take a look at this simple question. And sorry for the informal math language and equations, I hope you guys can understand it. So, depending on the case, I have 2 or 8 simple quadratic functions f(a), f(b), f(c),… f(z). Each a,b,c,…,z have a different...

If $\alpha,\,\beta,\,\gamma$ are the roots of the equation $x^3+ax+1=0$, where $a$ is a positive real number and $\dfrac{\alpha}{\beta},\,\dfrac{\beta}{\gamma},\,\dfrac{\gamma}{\alpha}$ be the roots of the equation $x^3+bx^2+cx-1=0$, find the minimum value of $\dfrac{|b|+|c|}{a}$.

from numpy import log as ln z = 3 k = 2 x = 1 - ln(1 + z) / ln(1 + k) y = 1/5 print("The x=", x) Q = x**y print(Q) The result is The x= -0.26185950714291484 c:\Users\-\Desktop\... RuntimeWarning: invalid value encountered in double_scalars Q =...

Could someone confirm my answer please?

I found, what appears to be, a good channel on General Relativity and other science topics. I'm dubious because... the internet. I'd love a second opinion on whether this channels first few videos on The Maths of General Relativity are doing it justice. I'm a dad with a day job and I can't...

In the example below, x is static while x1 is a dynamic copy of x. Also, y and z are similar expressions containing x and x1 respectively. If we evaluate expressions containing x and x1, they display in numeric and mathematical formats, respectively (y and z below). How can I display z as a...

it really took me time to figure out as to how that equation in aterisk was arrived at...i just noted that both sides of the equation were multiplied by ##-\frac {1}{3}## any particular reason for that? what is the common thinking around that? can one multiply both sides by say ##\frac {1}{6}##...

What "ampere value” is measured by a d-c ammeter when the current fluctuates rapidly?

since ##|z|≤3## →##z=0+0i##, therefore we shall have centre##(0,0)## and radius ##3##, find my sketch below,

m_1 = 1; C_p1 = 2219; T_1in = 100 + 273.15; T_1out = 75 + 273.15; Q_1 = (m_1)*C_p1*(T_1in-T_1out); while Q_1 ~= 30000 T_1outnew = T_1out + 0.1; Q_1 = (m_1)*C_p1*(T_1in-T_1outnew); T_1out = T_1outnew; end T_1outnew keeps increasing, but the code never stops; and naturally, Q...

For Example: Trial 1: 5.36 ± 0.03 Trial 2: 5.42 ± 0.04 Trial 3: 5.35 ± 0.01 Trial 4: 5.38 ± 0.03 Trial 5: 5.45 ± 0.02 What I did was take the average of the best estimates and the uncertainties. Best Value 5.39 ± 0.03 (0.03+0.04+0.01+0.03+0.02)/5=0.026=0.03

The source of the 0.824×10-4 value is http://hyperphysics.phy-astr.gsu.edu/hbase/Astro/denpar.html . I also looked at the Planck 2018, paper I but could not find a value for Ωr. I searched the internet with: radiation density cosmology friedmann omega but I had no success. I also looked at...

##\int_0^5 [-x^3+3x^2+6x-8\,]dx## ##\int_0^1 [-x^3+3x^2+6x-8\,]dx= |-\frac {17}{4}|## ##\int_1^4 [ -x^3+3x^2+6x-8\,]dx= 16## ##\int_4^5[-x^3+3x^2+6x-8\,]dx= |-\frac {49}{4}|## Therefore, total area is ##|-\frac {17}{4}|+ 16+|-\frac {49}{4}|=32.5## now where my problem is,... my colleague...

I may have misunderstood the expectation value, but if not then with the Copenhagen Interpretation it is easy to understand the expectation value for a wave function. It is just based on the probability of each event. If there were 4 possible events, and the probability of the event having a...

Hello everyone, I have to find an interval of this Riemann integral. Does anybody know the easiest way how to do it? I think we need to do something with denominator, enlarge it somehow. My another guess is the integral is always larger than 0 (A=0) because the whole function is still larger...

(1) For ##x>a## ##f(x)=x^2+x-a+1 \rightarrow## minimum value obtained when ##x=-\frac{1}{2}## Minimum value of ##f(x)=\frac{3}{4} -a## (2) For ##x<a## ##f(x)=x^2-x+a+1 \rightarrow## minimum value obtained when ##x=\frac{1}{2}## Minimum value of ##f(x)=\frac{3}{4}+a## But the teacher said...

##\frac {7}{2x+2}=\frac {4x-3}{-2x-2}## ##-7(2x+2)=(4x-3)(2x+2)## ##x^2+2x+1=0## ##x=1## or ##x=-1## can we also have; ##-7=4x-3## can the ##2x+2## cancel out? i am a bit mixed up on this very simple problem...and why am i getting false on my ti nsipre...

In the 3rd edition of the Introduction to Quantum Mechanics textbook by Griffiths, he normally does the notation of the expectation value as <x> for example. But, in Chapter 3 when he derives the uncertainity principle, he keeps the operator notation in the expectation value. See the pasted...

I have managed to find the gamma value using the following equation: (T2/T1)= (P2/P1)(gamma-1/gamma. This will give me the answer of 1.29 SF. After this step, I am clueless. Can someone help me with this question please? I assume we have to find the enthalpy at state 1 to do that question.

If the boundary condition is not provided in the form of electric potential, how do we solve such problem? In this case, I want to use ##V = - \int \vec{E} \cdot{d\vec{l}}##, but I don't know how to choose an appropriate reference point.

Hey all, So this time I have a different kind of question - namely, "what is this called?" I recall hearing/reading this in at least two places, one of which was YouTube. The idea is the following: A RNG picks an integer uniformly from 1 to N. It picks 4. What is the expected value of N? I'm...

Determine an interval in which the solution of the given initial value problem is certain to exist $t(t-4)y'+y=0 \quad y(2)=2\quad 0<t<4$ ok my first step was isolate y' s $y'=-\dfrac{y}{t(t-4)}$ not sure what direction to go since we are concerned about an interval

What does the phrase “Due to Lorentz invariance, only the Higgs particle can have a non-zero expected value in a vacuum” mean?

This confusion has lingered in the back of my mind for years now, would be good for me to finally get a grasp on this. Say I have an object currently at rest, and I use energy X to accelerate it to speed v. According to the standard formula, it now has a kinetic energy 1/2mv^2. Now I use the...

I am quite confused by this. I was sure that ω=3*sqrt(5)*10^6, because that is the coefficient of t, and generally u(x,y,z,t)=Asin(kx−ωt+ϕ) for a multi dimensional harmonic wave. However in the answers it is said that ω=3*sqrt(5)*10^14. I can't see the reason for that, could anyone explain please?

1. When n=1, u1+1=3-1/3(u1) u2=3-1/3(3) u2=2 When n=2 u2+1=3-1/3(u2) u3=3-1/3(2) u3=7/3 When n=3 u3+1=3-1/3(u3) u4=3-1/3(7/3) u4=20/9 The common ratio is defiend by r=un+1/un, but this is different between the terms, i.e. u2/u1=2/3 whereas u3/u2=(7/3)/2=7/6 Have I made a mistake? 2. A...

Hi all Simple question: How I can compute the value of \(a = \sin \left( 2017 \sqrt[5]{2} \right) \) under following assumptions: No use of advanced numerical libraries is allowed. Only accepted operations are: comparisons, absolute value, addition, subtraction, multiplication and division...

Let $a,\,b$ and $c$ be positive real numbers. Determine the minimum value of $\dfrac{a+3c}{a+2b+c}+\dfrac{4b}{a+b+2c}+\dfrac{8c}{a+b+3c}$.

In this text they are saying that rms value is square root of average value of i² but i am not able to relate this thing to equations they have given. It feels to me that the equations tell something different from the text. From text I interpret that if we add each and every value of i² from 0...

I tried to do it by derivative but there are two variables, so I don't know how to proceed. Does anyone know how I can solve it? Remembering that you don't need to find the value of ##\theta##. I just need to find a relationship between ##\theta_1## and ##\theta_2##

If the Summary is not clear, the following is an example translated from: https://telecombloger.ru/7335 '... air conditioning systems. For example, the efficiency of a compressor is about 85%. The remaining 15% is spent on friction, oil movement, overflows, heating, etc. The efficiency of the...

The principal equilibrium in a solution of NaHCO3 is HCO3-(aq) + HCO3-(aq) <-> H2CO3(aq) + CO32-(aq) Calculate the value of the equilibrium constant for this reaction. My solution: This overall reaction is the same as the sum of the following reactions: HCO3-(aq) <-> H2CO3(aq) + OH-(aq)...

Question: The national price of a good is distributed normally with mean £1.20, standard deviation 5p. Sample data is for price in London, determine whether there is sufficient evidence at 5% level to suggest that the mean price in London is different to the national mean. Standard deviation...

Hi In the book, "Why does E= mc2" by Cox and Forshaw, while discussing time dilation, the example of a muon is given. The authors explain that muons when circulated in the 14 m diameter AGS facility at Brookhaven at 99.94% of the speed of light, its lifetime is increased from the value of 2.2...

Here is the question: Is it true that the value of K depends on the amounts of reactants and/or products that are mixed together initially? Explain. This is my explanation: The reaction always shifts left or right given any initial reactant and product amounts to attain equilibrium. Thus, the...

If E(X1)>E(X2), does it mean that E(1/X1)<E(1/X2)? Thanks!

How can I find Cauchy principal value. of this integral \[ n(x) = \int_{a}^{b} \frac{d \omega}{\omega ' ^2 - x^2} \] Where $ a<x<b $ I case $a = 0, b = 3, x = 1$ We get \[ n(1) = \int_{0}^{3} \frac{d \omega}{\omega ' ^2 - 1^2} = −0.3465735902799727 \] The result shown is the Cauchy...