Derivation Definition and 1000 Threads

Homework Statement How do you get from (3.171) to (3.172)? In particular, why is ##\int e^{-ip.r/{\hbar}}\frac{p_{op}^2}{2m}\Psi(r,t)\,dr=\int\frac{p_{op}^2}{2m}[e^{-ip.r/{\hbar}}\Psi(r,t)]\,dr##? ##\,\,\,\,\,##-- (1) Homework Equations The Attempt at a Solution For (1) to be true, it...

Hello,*please refer to the table above. I started from x(n)=x(n*Ts)=x(t)*delta(t-nTs), how can we have finite terms for discrete time F.S can anyone provide me a derivation or proof for Discrete F.S.?

Homework Statement Homework Equations Maxwell relations The Attempt at a Solution Here is how I proceeded. Am I allowed to go from line 1 to 2? It almost seems too simple. dU=TdS-PdV \\ (\frac{\partial U}{\partial P})_T=T(\frac{\partial S}{\partial P})_T-P(\frac{\partial V}{\partial P})_T...

Does this derivation: ...imply: My best guess is that x(t) ≠ t So I would also guess that F(x(t)) ≠ F(t) But then how can this derivation be explained? How can F(x(t)) = m(a(t))? What does that actually mean? How come it's not: F(x(t)) = m(a(x(t))) ? Why/How does the x just cancel...

Hello good people, please refer to this: (notice the mistake in 9.31: cos(psi) switches places with cos(phi)sin(psi) to the best of my understanding) Now, I am trying to derive 9.30 and for this, according to the book, we solve 9.32. The problem is I can not understand 9.32, the meaning of...

Homework Statement what is y ′and y bar ? why y ′ is changed to y bar ? why are they = 0 ? Homework EquationsThe Attempt at a Solution

Hey I'm trying to follow the derivation given here: http://lampx.tugraz.at/~hadley/ss1/studentpresentations/Bloch08.pdf Homework Statement As it says in the pdf: "Based on Noether's theorem construct the energy-momentum tensor for classical electromagnetism from the above Lagrangian. L=-1/4...

The conserved 4-momentum operator for the complex scalar field ##\psi = \frac{1}{\sqrt{2}}(\psi_1 + i\psi_2)## is given in terms of the mode operators in ##\psi## and ##\psi^{\dagger}## as $$P^{\nu} = \int \frac{d^3 p}{(2\pi)^3 }\frac{1}{2 \omega(p)} p^{\nu} (a^{\dagger}(p) a(p) +...

A few decades ago my algebra teacher showed how to construct the expression for binomial coefficients. If I start with Pascal's recursion, and propose C(n,k)=n!/k!(n-k)!, I can prove it to be so through induction. But that doesn't give me that happy feeling that comes with understanding. It...

At time 1:11:20, Lenny introduces the metric for ordinary flat space in the hyperbolic version of polar coordinates? Is that what he is doing here? d(tau)^2 = ρ^2 dω^2 - dρ^2. He then goes on to say that this metric is the hyperbolic version of the same formula for Cartesian space, i. e...

How do you derive it? I'm looking for the form J = -D(dC/dX) From the image, I am assuming left side is of higher concentration. N represents the number of molecules. My work: Mass balance Net molecules in from concentration gradient = Net = N(x) - N(x+Delta X) Net concentration in =...

please check the video at 5:33. how can we find the partial derivative w.r.t n1 n2 and on? isn't each state (n1, n2 and on) one discrete state not a continuous variable? is it because we can have multiple particles in the given energy state? However its a finite discrete number. as far as I...

I did everything I could to solve the following problem: A solid ball of radius rb has a uniform charge density ρ. What is the magnitude of the electric field E(r) at a distance r>rb from the center of the ball? E(r) = My third attempt went like this: qencl=[ρ(4/3)(π)rb3]...

Consider a system of two charges ## q_1## and ##q_2## separated by distance ##r_1##.This configuration is associated with a potential energy ##U_1##.When the separation is increased to ##r_2##.Potential energy becomes ##U_2## ##dW_E##=##\vec{F}##.##\vec{dr}##...

Homework Statement So I attached the page from the lab with the directions for the derivation. It may be easier to view that document. The lab was set up was taking two objects and rolling them down an incline. The time was measured using photo gates. Basically, I need to use conservation of...

Hi, I've attached a file displaying a derivation to make the kinetic energy of a two-body problem into a kinetic energy only involving the reduced mass. When plugging 8.3 into 8.1, I just don't quite see how this derivation makes sense. Shouldn't there be a $$ \mu^2$$ term? Since when squaring...

I've attempted to derive an expression for the Christoffel symbols (of the 2nd kind) solely in terms of the covariant and contravariant forms of the metric by only using the definition of the Christoffel symbols. I would like to know if my approach is correct or not. The Christoffel symbols are...

Homework Statement Hi guys; I'm just dealing with Fourier series and they evaluate integrals such as ∫sin(nπx/L)dx from 0 to L as (L/nπ)[1-(-1)^n]. Can someone please tell me how to get to this conclusion or point me in the direction of a resource that will show me? Additionally I need to solve...

http://ecee.colorado.edu/~bart/book/book/chapter2/pdf/ch2_5_5.pdfcan you please tell me where f/(f(gi,fi) is from? and also how to get to (2.5.13)

Homework Statement Homework Equations Chain rule, partial derivation The Attempt at a Solution dv/dt=dv/dx*dx/dt+dv/dy*dy/dt dx/dt=-4t -> evaluate at (1,1) =-4 dv/dt=-4dv/dx+4(-2) dv/dt=-4dv/dx-8 How can I find the missing dv/dx in order to get a value for dv/dt? Thanks!

Hello All, In GR the factor 8piG/c^4. I want to understand how the term is derived? I mean to say that is this related to Friedmann Equation. How the factor actually comes into Einstein's field equation? I am sorry if I am unable frame the question properly. Thanks. -- Shounak

Homework Statement 1. Show that the Lorentz algebra generator ##J^{\mu \nu} = i(x^{\mu}\partial^{\nu}-x^{\nu}\partial^{\mu})## lead to the commutation relation ##[J^{\mu \nu}, J^{\rho \sigma}] = i(g^{\nu \rho}J^{\mu \sigma} - g^{\mu \rho}J^{\nu \sigma}-g^{\nu \sigma}J^{\mu \rho}+g^{\mu...

From P. Meystre's book elements of quantum optics (Many labels of equations are wrong:H) Page 83, the annihilation operator and creation operator, which are helpful to discuss harmonic oscillator, are defined as ## a=\frac{1}{\sqrt{2\hbar\Omega}}(\Omega q+ip),\\...

I'm having trouble deriving equation (2.45) on page 25. In particular, in the derivation of ##i\frac{\partial}{\partial t}\pi({\bf{x}},t) = -i(-\nabla^{2}+m^{2}) \phi({\bf{x}},t)##, I need to show that ##\frac{1}{2}\pi({\bf{x}},t) \phi({\bf{x'}},t)(-\nabla^{2}+m^{2}) \phi({\bf{x'}},t) -...

I have starting working through section 134 of Landau and Lifshitz, vol 6, and it seems I have entered some kind of twilight zone where all my math/physics skills have left me :cry: The derivation starts with the energy-momentum tensor for an ideal fluid: ## T^{ik} = wu^i u^k - p g^{ik} ##...

http://quantumfreak.com/derivation-of-pvnrt-the-equation-of-ideal-gas/please check eq.(7) pressure equation is P=F/A which means, in any region over the surface, pressure will be the same. for example, if we assume all the particles have the same mean squared velocity, pressure of one cube will...

1. Derive this equation t = 2(vi)/g*sin(theta) where vi isinitial velocity, and g is acceleration due to gravity 2. Implicit differentiation, possibly gravity as a constant.The Attempt at a Solution t = 2(vi)/v*sin(theta) dt/d(theta) = 2(vi)/g * dt/d(theta)(sin(theta)) dt/d(theta) = 2(vi)/g *...

Hello there ! I need to derive the formula of first order correction to the energy in the case of discrete level of wave function with descrete spectrum.

The Joule coefficient, μJ, is defined as μ = (∂T/∂V)U. Show that μJ CV = p – αT/κ Relevant equations Cv=(∂U/∂T)v κT=-1/V*(∂V/∂p)T α=1/V*(∂V/∂T)p dV(T,p)=(∂V/∂T)pdt+(∂V/∂p)TdpWhat I have attempted was to make μ = (∂T/∂V)U=(∂T/∂U)V(∂U/∂V)T=(∂U/∂V)T*Cv-1. Then α/κT=(∂V/∂T)p/(∂V/∂p)T because the...

Hi, I was just looking over my textbook, and it mentions a ## \Delta##-y and y-## \Delta## transformation that is helpful for dealing with circuits in these configurations. The equations can be found here...

Homework Statement There's a derivation here that I'm looking at, and I've hit a snag. At (1) about 15 lines down the page, the author divides by Δx and takes the limit as Δx goes to 0. I understand what he did on the right side of the equation, but on the left side of the equation, by what...

Is there some mathematical derivation for calculating the orbital velocity based on altitude and acceleration without using calculus? I thought of equations of motion, but I always get problems. Is there a way to derive it using laws of gravitational potential and kinetic energy ? Are the...

Hi, I feel sometimes when I'm doing calculus I lose the logic and intuition behind what I'm doing, especially when integrating. I have yet to find a way to think about it in a way it makes sense to me why the definite integral would tell us the area under a curve. Same with why the second...

Homework Statement Find tangent line of y=xe^{\frac{1}{x}} at point x=\alpha and it's limit position when \alpha \rightarrow +\infty. Homework Equations Tangent of y=f(x) at point M(x_0,f(x_0)): y-y_0=f^{'}(x_0)(x-x_0) The Attempt at a Solution Applying the above equation for tangent of...

A charge Q is placed at a distance a = 3m and a charge q is placed at a distance b For what value(s) of b is the x-component of the force maximized? I know to maximize the force we need to maximize F_Qq = k Qq b/(3^2 + b^2)^{3/2}. To do this we need to set the first derivative to zero and...

I was wondering how to derive the sinusoidal equation for the simple armonic oscillator. But I am currently trying to understand this step in this webpage: I don't get where do P and Q come from and why it is summing pe^iwt + qe^-iwt. please I need some help. The rest of it pretty much makes...

Can anyone explain how to take the derivative of (Aδij),j? I know that since there is a repeating subscript I have to do the summation then take the derivative, but I am not sure how to go about that process because there are two subscripts (i and j) and that it is the Kronecker's Delta (not...

In some reading I came across this equation P/P1=(T/T1)^-g/aR which can apparently be derived from dp/P=(-g/RT)dh when T=T1 + a(h-h1). I don't really understand how they could have taken the a out of the integral in order for it to be part of the exponent once you get rid the the ln on both...

Homework Statement The momentum carried by an electromagnetic field is [;\vec{P}(\vec{x}, t) = \frac{1}{4\pi c} \int d\vec{x}\vec{E}(\vec{x},t) \times \vec{B}(\vec{x},t);] show that for a finite field extension [;\vec{J}(\vec{x}, t) = \frac{1}{4\pi c}\int -i...

Hello, This is probably a very easy questions about the one-dimension momentum operator derivation. So you take the d<x>/dt to find the "velocity" of the expectation value. At one point in the derivation early on, you bring in the d/dt into the integral of the expectation value. The book I'm...

How is it derived? The cutoff frequency is Fc = 1/2piRC. R = resistance, C = capacitance. I read somewhere it has to do with Laplace Transforms, but I'm not sure where to go from here. It kind of irks me to just accept this equation without some proof. Thanks!

Homework Statement Using the special relativity formulae p = mv / [1 - (v/c)2] E2 = p2c2 + m2c4 derive linear relations between: (i) momentum and mass; (ii) energy and mass; (iii) energy and momentum, which involve only c, c2, β = v/c, and γ (= 1/sqrt(1 - β2)) The attempt at a solution I am...

Hi! I have performed an experiment measure force on a wire with electric current in a magnetic field. I got 3 graphs: Force as function of length (L) of wire, Force as function of current (I) and Force as function of magnetic field (B). In all cases, I got approximately a straight line through...

Homework Statement Good Day, On an oscilloscope, when two incoming signals are out of phase, in an XY setting, an ellipse appears on the oscilloscope screen. The phase shift between the two incoming signals can be found by the formula: sin^{-1}((Y_{max})/(Y_{int})) where Y max is the...

First by "this derivation" I'm referring to an online tutorial: http://farside.ph.utexas.edu/teaching/336L/Fluidhtml/node9.html It's said in the above tutorial that the ##i-th## component of the total torque acting on a fluid element is ##\tau_i = \int_V \epsilon_{ijk} \cdot x_{j} \cdot F_{k}...

there are no electromagnetic waves? All I know is that there is a modified version of the Maxwell equations (in differential form) for such a universe, such as (the arrows represent vector arrows): →∇x →B = μ0 →j + μ0 ε0 ∂→B/∂t instead of having ∂E/dt in the last term (which would be the case...

Homework Statement A heavy mallet of Mass M (see Attached file) is dropped and moves through vertical distance y before it hits the top of a tent stake of mass m, driving it into the ground a distance d. Assume that the ground offers a a constant resistance to the motion of the tent stake and...

I understand that Gott derived a formula for calculating the size of the observable universe, and the value of the diameter based on current obsrvations is 93 Gly. Can someone please show the mathematical derivation of Gott's formula, or give a reference to a source which shows this derivation?

Homework Statement I am trying to derive the curvature tensor by finding the commutator of two covariant derivatives. I think I've got it, but my head is spinning with Nablas and indices. Would anyone be willing to check my work? Thanks Homework Equations I am trying to derive the curvature...

Hope this derivation helps someone!