Value Definition and 1000 Threads

Homework Statement A wavelenght of 410.2*10^-9m is emitted by the hydrogen atom in a high voltage discharge tube. what are the initial and final values of the quantum number n for the energy lvl transition that produces this wavelength? Homework Equations 1/(lambda) = R * (1/2^2 - 1/n^2)...

What are the value additions of GR ? What does it give more than "SR + Newtonian Gravity" gave? Just want to see if someone has listed the same. I understand it gives a beautiful framework/idea for defining geometry of space time based on mass+energy sources and drafting law of motion of...

Homework Statement Using J^2 \mid j,m_z \rangle = h^2 j(j+1) \mid j,m_z \rangle J_z \mid j,m_z \rangle = hm_z \mid j,m_z \rangle Derive that : \langle j,m_z \mid J_-J_+ \mid j,m_z \rangle = h^2[ j(j+1) - m_z(m_z+1)] Homework Equations J_- = J_x - iJ_y J_+ = J_x + iJ_y The...

Mean Value Theorem Suppose that ##f## is a function that is continuous on ##[a,b]## and differentiable on ##(a,b)##. Then there is at least one ##c## in ##(a,b)## such that: $$f'(c) = \frac{f(b) - f(a)}{b - a}$$ My question is: wouldn't it be better to state that ##c## is in ##[a,b]## rather...

Can we integrate: $$\int_a^b |x| dx$$ using an antiderivative of ##|x|##, namely ##\frac{1}{2} x |x|##, instead of splitting up the integration interval? I know this is not particularly useful for integrals such as: $$\int_{-5}^5 |t^3 - 8| dt$$ However, for absolute value functions with linear...

Hello everyone. Let us consider two fermions whose spin state wave functions are certain (normalized) ##\psi_{1}## and ##\psi_{2}##. So the overall normalized spin state wave function of this system is of the form: ##\psi = (1/\sqrt{2})(\psi_{1} \psi_{2} - \psi_{2} \psi_{1})## Is there any...

So I'm interested in calculating the Spearman correlation matrix, but I am running into some issues. All of the examples I have found only calculate rho scores between two columns. I am trying to replicate results from a white paper...

Hey, I'm stuck halfway through the solution it seems. I could use some tips on how to continue. 1. Homework Statement I have to determine a linear combination of the states |0\rangle, |1\rangle, of a one dimensional harmonic oscillator, so that the expectation value \langle x \rangle is a...

Hey! :o Prove using Green's theorem that the boundary value problem $$\frac{\partial}{\partial{x}}\left ( (1+x^2)\frac{\partial{u}}{\partial{x}}\right )+\frac{\partial}{\partial{y}}\left ( (1+x^2+y^2)\frac{\partial{u}}{\partial{y}}\right ) -(1+x^2+y^4)u=f(x,y), x^2+y^2<1 \\ u(x, y)=g(x,y)...

Solve the boundary value problem: $\left\{ \begin{array}{lcl} y''&=&0,\hspace{1.0mm} 1<x<2\\ y(1)&=&0\\ y(3)+y'(3)&=&0 \end{array} \right. $ For the problem, I first calculate the eigenvalues and after check the roots and finally find the eigenvectors. Is correct this? Help me please :).

Homework Statement Consider the following inital states of the symmetric 2D harmonic oscillator ket (phi 1) = 1/sqrt(2) (ket(0)_x ket(1)_y + ket (1)_x ket (0)_y) ket (phi 2) = 1/sqrt(2) (ket(0)_x ket(0)_y + ket (1)_x ket (0)_y) Calculate the <p_x (t)> for each state Homework EquationsThe...

Homework Statement Table gives the rectilinear motion of a 4kg mass over a 5 s time interval. When the time was 3.8 seconds, the velocity of the mass was approximately what Homework EquationsThe Attempt at a Solution I first just tried to find the average of the velocities at 3.5 and 4.0...

Homework Statement Suppose, the following equation describes the relation between an independent and a dependent variable physical quantities(that will be measured by experiments; for example, temperature, current, voltage etc) x & y : ##y = ax^2 + bx + c## We have to find the values of the...

Homework Statement Find a power series representation for the function below & determine the radius of convergence. f (x)=(1+x)/(1-x)2 2.Relevant equation Shown in attached image below which is the solution the problem. 3.The attempt at a solution I'm trying to fathom the solution here...

What is the value of curvature which caused by earth(geodetic effect) on space-time?

Mod note: I revised the code below slightly, changing the loop control variable i to either j or k. The reason for this is that the browser mistakes the letter i in brackets for the BBCode italics tag, which causes some array expressions to partially disappear. Hello, I am trying for the first...

Hi. I was just curious about the current value of the cosmological constant. My astrophysics class lecture notes say on the order of 10^-122, but the Wikipedia article says 10^-35 s^-2. Could someone explain where the 10^-35 s^-2 value comes from? Thanks!

how do i evaluate say a definite integral from [-3,3] of |x+1|? Any advice? I'm so confused.

Hey! :o We have the following initial value problem: $$x' = \frac{1}{2}(45 − x) + \frac{1}{4}(y − x) \\ y' = \frac{1}{4}(x − y) + \frac{1}{2}(35 − y) + \frac{1}{2}(z − y) + 20 \\ z' = \frac{1}{2}(y − z) + \frac{1}{2}(35 − z)$$ This can be written as follows: $$\begin{pmatrix} x\\ y\\...

Let $A,\,B$ be acute angles such that $\tan B=2015\sin A \cos A-2015\sin^2 A \tan B$. Find the greatest possible value of $\tan B$.

Homework Statement Show that E must exceed the minimum value for V(x) for every normalizable solution to the TISE, Hψ = Eψ Hint: rewrite the TISE as d2ψ/dx2 = (2m/ħ)(V(x) - E) Homework Equations I understand how to get the TISE Hψ = Eψ into the form of the hint by using the hamiltonian and...

I know that the following is true and I've already proven it. Let $Y$ be a random variable and $\varphi$ a measurable function. Let $A$ be a $\Sigma_Y$ measurable set. If $ X (\omega) = \varphi(Y (\omega))$ for all $\omega\in A $ , then $\mathbb{E}(X|Y )(\omega) = \varphi(Y (\omega))$ for...

Homework Statement $$ \int_0^{\pi} \frac{x(sinx)^{2n}}{(sinx)^{2n}+(cosx)^{2n}} $$ = A) π2 B) 2π2 C) π2/4 D) π/2 Homework Equations $$ \int_0^π f(x)dx = \int_0^π f(a-x)dx $$ The Attempt at a Solution If we put n = 1, we get the C option π2/4 But is it true for all n?

Homework Statement If a,b,c are three -zero vectors such that each one of them are perpendicular to the sum of the other two vectors, then the value of | a, b, c|2 is |a|2 + |b|2 + |c|2 |a| + |b| + |c| 2(|a|2 + |b|2 + |c|2) ½(|a|2 + |b|2 + |c|2) Homework Equations a.b = ab cosθ |axb|= ab sinθ...

Homework Statement Consider the equation: 3logx5+2logx2-log1/x2=3 a)State which values of x for which the equation is defined. b)Solve the equation for x. Homework EquationsThe Attempt at a Solution 3logx5+2logx2-log1/x2=3 =logx53+logx22-log1/x2=3 =logx125+logx4-log1/x2=3 =logx500-log1/x2=3...

Let (-3, 2) be a point on the terminal side of θ. Find exact values of cosθ, cscθ, and tanθ? Can anyone help!?

Let $[a,b]$ be a closed real interval. Let $f:[a,b] \to \mathbb{C}$ be a continuous complex-valued function. Then $$\bigg|\int_{b}^{a} f(t)dt \ \bigg| \leq \int_{b}^{a} \bigg|f(t)\bigg| dt,$$ where the first integral is a complex integral, and the second integral is a definite real integral...

What is the unit value of coulomb constant(k)? I just want to know the CGS unit value of k. In my book it is said the CGS unit value of k is 1. By i don't know how it come.?

so I'm doing a little project in solar thermal energy and I want to do the calculations before I start anything. I am stuck on getting the value of the pressure of the water inside the absorber when the temreture gets to 350 C. Is there a way to calculate it using thermodynamics table or...

Homework Statement I read this line in my textbook: "##PbS,CdS## are precipated in dilute solution only due to higher ##K_{sp}##" And I googled about the relation between solubility and ##K_{sp}## and I found that: "More is the ##K_{sp}## of a salt more it is soluble in a solution(I think...

In ring theory, a polynomial over a rings, say ## R[x] ## is presented as an abstract object of the form: ## p(x) = a_{n}x^{n} + ...+ a_{1}x + a_{0} ## where the coefficients ## a_{n}...a_{0} ## are from a ring R with unity and ##x## is a formal symbol. So what is the significance of ## p(x+1)...

Homework Statement Demonstrate that the expectation value of momentum (p) for the wave function: ψ(x)∝e^(-γx) when x>0, ψ(x)=0 when x<0. Hint: Pay special attention to the discontinuity at x=0.[/B] Homework Equations <p>=<ψ|p|ψ>=∫dxψ*(x)[-iħ∂/∂x]ψ(x) from -∞ to ∞. [/B]The Attempt at a...

Homework Statement Homework Equations The Attempt at a Solution http://imgur.com/7TRWjBg I don't really get what it's asking. I don't know how to define a Fourier series when the boundaries for X are between non-multiples of Pi. On top of that, it has one boundary that has 4<x<2Pi. How can...

Hello, I've been trying to find <p'|φ(x)|p> for a free scalar field. and integral of <p'|φ(x)φ(x)|p> over 3d in doing the space In writing φ(x) as In doing the first, I get the creation and annihilation operators acting on |p> giving |p+1> and |p-1> which are different from the bra state |p>...

For any positive real numbers a, b such that $a+b=1$, the inequality $(1+\frac{1}{a})(1+\frac{1}{b})\ge k$. Find the maximum value of $k \in \Bbb{R}$. I did: $(1+\frac{1}{a})(1+\frac{1}{b})= \frac{a+1}{a} \cdot \frac{b+1}{b}=\frac{ab+a+b+1}{ab}= 1+\frac{2}{ab} \ge k$ Using the Cauchy's...

Hey! :o We have the initial and boundary value problem $$u_{xx}(x,y)+u_{yy}(x,y)=0 , x^2+y^2<1 \\ u(x,y)=0 \\ u(1, \theta)=\sin{\theta}, 0< \theta< \pi$$ $$U_{\rho \rho}(\rho, \theta)+ \frac{1}{\rho^2} U_{\theta \theta}=0, 0< \rho<1, 0< \theta< \pi$$ We are looking for solutions of the form...

Homework Statement Finding the critical value of shear stress at the junction and at the neutral axis Homework Equations stress max = (Bending moment x height from neutral axis)/Moment of inertia Shear stress = Shear force/area The Attempt at a Solution I am able to do the first 2 parts but...

Homework Statement The largest value of r for which the region represented by the set { ω ε C / |ω - 4 - i| ≤ r} is contained in the region represented by the set { z ε C / |z - 1| ≤ |z + i|}, is equal to : √17 2√2 3/2 √2 5/2 √2 Homework Equations complex number = a + ib where a,b ε R The...

I'm trying find the minimal polynomial of a=3^{1/3}+9^{1/3} over the rational numbers. I am currently going about this by trying to construct a polynomial from a (using what I intuitively feel would be a sufficiently small number of operations). Then I'd show it's irreducible by decomposing it...

In the wikipedia page of Lorentz Transformation (http://en.wikipedia.org/wiki/Lorentz_transformation#Lorentz_transformation_for_frames_in_standard_configuration) it's said that The problem I'm having here is that while taking Lorentz Transformation as true, I failed to verify the statement...

Find the maximum integral value of $k$ such that $(k-4)(x^2+x+1)^2-(k-3)(x^2+x+1)(x^2+x+2)+(x^2+x+2)^2=0$ has at least one real root for $x$.

Determine the minimum of $y$ where $y=|x-1|+|2x-1|+|3x-1|+\cdots+|nx-1|$.

Homework Statement Show that sin(2θ) / (1 + cos(2θ) = tan(θ) - I've completed this part Hence find the value of cot(π/8) in the form a + b√(2), where a, b ∈ ℤ Homework Equations cot(θ) = (1 + cos(2θ)) / sin(2θ) The Attempt at a Solution I did the math, got (1 + cos(π/4)) / sin(π/4) = (1 +...

Homework Statement The potential difference Δϕ between the plates of a spherical capacitor is kept constant. Show that the electric field at the surface of the inner sphere will be a minimum at a = b/2, where a is the radius of the inner sphere and b is the radius of the outer sphere. Homework...

Hello, I am analysing hydrology data and curve fitting to check the best probability distribution among 8 candidate distribution. (2 and 3 parameter distributions) The selection is based on the lowest AIC value. While doing my calculation in excel, how is it suggested to treat very low (approx...

I want to take the arg max over a number of functions as below, however it is possible that there are multiple i's for which the result is maximal. How do i denote that I want to take the last possible i, for example if it results in 3 and 5 I want it to return 5, is there notation available for...

Particularly, I mean trained skills rather than traits. For example, for a blank student/graduate who knows only physics theory, learning LaTeX would put them a little bit ahead. Then maybe some programming, learning simulation software etc. I'm finishing up my 2nd year in undergraduate right...

Homework Statement Prove the Mean Value Theorem for integrals by applying the Mean Value Theorem for derivatives to the function F(x) = \int_a^x \, f(t) \, dt Homework Equations [/B] Mean Value Theorem for integrals: If f is continuous on [a, b], then there exists a number c in [a, b]...

Hi all, Here is my story. My school offers BA and BS for both physics and math. I am currently a junior in the BS programs for both physics and math. The only difference between the two are merely the language courses verses the two science and society courses (S&SC). I have been told about the...