Derivation Definition and 1000 Threads

equation -- Wave Equation Derivation Question Hello, my teacher says that if, on a wave equation f(x-ct)=f(e) then \partial_{ee}= \partial_{tt}- c^2 \partial_{xx} but i think that \partial_{t}=\frac{\partial }{\partial e} \frac{\partial e}{\partial t}=-c\frac{\partial }{\partial e} and...

Homework Statement This is a derivation of the relation between solubility of a salt and pH of the solution in which it is dissolved from our textbook. Consider a salt MX whose Ksp=[M+][K-] If this were dissolved in a solution of the acid HX whose Ka=[H+][X-]/[HX] then what would be its...

Most of the book using PV=nRT for PV^gamma constant for adiabatic process. However, please refer attachment, proving using conservation of energy will also make sense?

I would like to derive the air resistance equation showed in the attached photo. A little while ago, I tried asking at a different forum, however, the users were very experienced and omitted several stages of the derivation, and thereby made the interpretation difficult as I am new to math, but...

This result will shortly revolutionize physics. This short paper breaks the barrier which has kept time as a C-number in the quantum theory while the other spacetime dimensions are operators. Amazing! http://vixra.org/abs/1209.0010 ABSTRACT: A non-unitary quantum theory describing the...

In our formulation of work done by a Force we say it is ∫ F.dl ... My knowledge of integration means adding Infinitesimal parts. We write dl because it is the smallest part of the distance moved. My question is why have we written F and not dF... Thanks for clarifying!

Hi PF, I have 2 doubts : 1. Can anyone give me the derivation of series below : X = 1 + 2n + 3 n^2 + 4 n^3 + ..... 2. I can do this series reverse if the result is given, using Mc'laurin series, but then came doubt regarding derivation of Taylor series. How do...

Folks, I am puzzled how the linear interpolation functions (see attached) were determined based on the following equation below ##\displaystyle...

Hi, I'm having a bit of difficulty deriving the time to max activity for the case of transient equilibrium for a parent-daughter. This is where I want to get to , tm = (1 / (λ1-λ2)) * 1n(λ1/λ2) I believe there is an alternative equation for tm as well expressed in terms of half-life...

I had 1 year ago a little discussion with DaleSpam about the short Lorentz derivation (triangle) if a photon alone can be seen as a light beam. 1) The long Lorentz derivation seems me correct, so no discussion about that 2) For the short Lorentz derivation with the triangle (c.t , v.t and...

In the attached snip, the last few steps of the lagrangian equation is shown. I don't understand how the \frac{\delta V}{\delta\dot{q_j}}= 0. As an example let me take gravitational force. With change in velocity ( along the downwards direction obviously), there sure is a change in gravitational...

First, energy of a disk: \int \frac{dm}{2}r^2 \omega^2 =\frac{\omega^2}{2}\int_0^R m\frac{2 \pi r dr}{\pi R^2}r^2 =\frac{m\omega^2}{ R^2}\int_0^R r^3 dr=\frac{m\omega^2 R^2}{4 } Which agrees with other sources. However, in the following lies my problem: The equation for a circle...

Hello, I am currently reading about the topic mentioned in the title of this thread. For the most part, I understand the derivation; however, at the end of the derivation, the author adds one little condition: "Where is the energy in a parallel plate capacitor actually stored? Well, if we...

With reference to this diagram, my textbook tells me the following: I am able to follow the rest of the derivation after this point, but I do not understand where equation 15.14 came from? I'm trying to think in terms of small angle approximations, but nothing is really coming of that...

My question regards how the approximation becomes an equality.

Homework Statement I'm working through a derivation for work in Thornton's Classical Dynamics but I'm stuck at one step. \begin{align} \vec{F} \cdot d\vec{r} &= m\frac{d\vec{v}}{dt} \cdot \frac{d\vec{r}}{dt}dt = m\frac{d\vec{v}}{dt} \cdot \vec{v}dt \\ &= \frac{m}{2}\frac{d}{dt}(\vec{v}\cdot...

Homework Statement I am unsure as to a step in Griffiths's derivation of the quantum harmonic oscillator. In particular, I am wondering how he arrived at the equations at the top of the second attached photo, from the last equation (at the bottom) of the first photo (which is the recursion...

Hi, The derivation of the Gravitational Potential formula, as I understand, is: W = Fd (1) W = G \frac{M_1m_2}{r^2}d (2) Substituting the Gravitational Force formula W = - \int_R^∞G \frac{M_1m_2}{r^2} \, dr (3) Integrating within the boundaries of the initial distance (R) and...

Homework Statement For a zero initial deflection and for a finite initial velocity, the time dependence of the vibration response of an overdamped system to an impulse is given by: (1) θ(t)=[I/(mω)√(ζ^2-1)][e^-(ζωt)][cosh(ω√(ζ^2-1))t] which for large values of time becomes: (2)...

Hello, I hear a lot about the Born rule ##P = |\psi|^2## where ##P## is a probability of a particle appearing at some location and ##\psi## is a wave function. When i look at double slit experiment interference pattern it seems to me that the pattern by itself already represents the...

Hey there guys! So we know that in linearized GR we work with small perturbations \gamma _{ab} of the background flat minkowski metric. In deriving the linearized field equations the quantity \bar{\gamma _{ab}} = \gamma _{ab} - \frac{1}{2}\eta _{ab}\gamma is usually defined, where \gamma =...

Given a wave: e(t)=\hat x E_{x0}\cos \omega t+\hat y E_{y0}\cos( \omega t+ \delta)[SIZE="4"](1) The book claimed: \sin^2\delta\;=\; \left[\frac {e_x(t)}{E_{x0}}\right]^2-2\left[\frac {e_x(t)}{E_{x0}}\right]\left[\frac {e_y(t)}{E_{y0}}\right]\cos\delta+ \left[\frac {e_y(t)}{E_{y0}}\right]^2...

I mean the binomial formula is something of the form ##\left(a+b\right)^n## = ##\sum_{i=1}^{n}\dbinom{n}{k}a^{n}b^{n-k}## and then you have the linear map ##\psi : A \rightarrow A## which is a derivation when; ##\theta(xy) = y\theta(x) + x\theta(y)## for all x,y in A so the leibniz formula...

Homework Statement In figure, the pulleys and the cod are light, all surfaces are frictionless, and the cord does not stretch. a) How does the acceleration of block 1 compare with the acceleration of block 2? The mass of block 2 is m2 = 1.3 kg. Derive an expression for the acceleration of...

(maybe this should go in the math section?) Homework Statement I'm supposed to derive the k.p form of the Schroedinger equation by plugging in the Bloch wavefunction expansion. But my actual question is just about the math. Homework Equations So when I plugged Bloch into the SE, one of the...

Hi, guys. I was wondering on Newton's Gravity Law derivation, and I found this page: http://www.relativitycalculator.com/Newton_Universal_Gravity_Law.shtml Everything seems clear, but the first step is just killing me, because I can't get it. Assuming small incremental changes in s...

Problem: In beginning mechanics physics labs, it is very often the case that you get large experimental error. This can be due to a number of factors, friction, of course, being a major player. However, it can also be the case that you might be comparing apples to oranges. For example, if you're...

Hi, my first thread. The Hawking temperature for a BH can be derived through compactifying the timelike dimension and hence identifying the time coordinate of the euclidean metric such as a periodic coordinate τ with period β. Now, very interestingly in the context of AdS/CFT correspondence...

Hi all, Del = i ∂/∂x + j ∂/∂y + k ∂/∂z in x y z cordinate similarly I require to see the derivation of del in other coordinates too. Please give me a link for the derivation.

Homework Statement A spring with stiffness k and unstretched length L is stretched so the elongation is d = x2 - L. A force is applied to make the final length of the spring x2. What is the work done by the force in terms of d? Homework Equations W = F * d = F*dx d = x2 - L F = k*dx...

This is not a homework question. This is not for a course. However, I got a warning for posting such questions elsewhere, so, I suppose I must post them here. Homework Statement The following is an excerpt of the derivation of the Schrodinger equation. After deriving the Klein-Gordon...

Homework Statement When deriving the intensity of an electromagnetic wave in my textbook, there was a part I didn't quite get. It's how I = Watts/m^2 becomes I= u c My textbook gave an example of a electromagnetic wave through a cylinder, with cross-section area A. In 1 second it would...

Homework Statement I am trying to derive the formula a_r=\frac{v^2}{r} for uniform circular motion (for personal understanding, this is not an assignment). But am having some difficulty. I have seen other proofs, but I want to know why my approach is wrong. The Attempt at a Solution...

I'm reading Spacetime and Geometry: An Introduction to General Relativity by Sean M. Carrol and in the chapter on gravitation, he derives the Einstein Field Equations. Here is the part I don't get. He starts with the equation R_{\mu\nu}-\frac{1}{2} Rg_{\mu\nu}=\kappa T_{\mu\nu} Wher R_{\mu\nu}...

Hi, This is not related with a specific homework question. I was studying this topic and have noticed that I didn't understand some bits.The car is negotiating a bend with a speed of V. The slope of the banket is θ The coefficient of friction is η Weight of the car if mg Radius of the bend is R...

Here and there I come across the following formula for the Lagrangian density of a real scalar field, but not a deriviation. \mathcal{L} = \frac {1}{2} [ \dot \phi ^2 - ( \nabla \phi ) ^2 - (m \phi )^2 ] Could someone show me where this comes from? The m squared term in particular...

Homework Statement Derive the formula for rod's moment of inertia: I = ml2/12 Homework Equations I = ml2/12 The Attempt at a Solution The only one derivation I know of is dividing the rod into two parts and then integrating from 0 to l/2. However' I'd love to know if there's some...

Homework Statement Derive the following relation, where z1 and z2 are arbitrary complex numbers |z1z2*+z1*z2| ≤ 2|z1z2| The Attempt at a Solution I found the expression |z1z2*+z1*z2| = |2(a1a2+b1b2)| = √(4[a12a22 + 2a1a2b1b2 +b12b22]) But that is where I get stuck. How does the...

Homework Statement On page 251 of Griffiths's quantum book, when deriving a result in first-order perturbation theory, the author makes the claim that <\psi^0|H^0\psi^1> = <H^0\psi^0|\psi^1> where H^0 is the unperturbed Hamiltonian and \psi^0 and \psi^1 are the unperturbed wavefunction and its...

I kindly ask for assistance in derivation of the equation for instantaneous power in an electric circuit, P(t) = V(t) I(t). I want to derive it as rigorously as possible. Here's what I got: We start with P = {\bf F} \cdot {\bf v}, where {\bf v} = \frac{d\bf r}{dt} We know that the force...

"use geometry"--Redshift derivation? 1. Use geometry to derive z=v/c where c is the speed of light and z = [v(obs)-v(em)]/v(em). Homework Equations None given... Though I am assuming that I am constant. The Attempt at a Solution I believe it has to do with the Doppler effect which...

In working out the derivation of the probability current density, I see (based on the definition of j(x,t)) that the limits of integration are changed from d/dt∫(b to a) P(x.t) dx = iħ/2m[ψ*(x.t)∂/∂xψ(x.t) - ψ(x.t)∂/∂xψ*(x.t)](b to a) to d/dt∫(b to a) P(x.t) dx =...

Homework Statement Derive the ripple voltage of a full-wave rectifier with a capacitor-input filter. Homework Equations Where V_{r(pp)} is the peak-to-peak ripple voltage and V_{DC} is the dc (average) value of the filter's output voltage. And V_{p(rect)} is the unfiltered peak rectified...

This is not a home work, it is part of the textbook on elliptical polarization. Attached is a page in Kraus Antenna book, I cannot verify the equation on the last line. Here is my work E_y=E_2(\sin{\omega} t \cos \delta \;+\; \cos \omega {t} \sin \delta) , \sin\omega {t} =\frac {E_x}{E_1}\;,\...

I'm in a high school pre-calculus class and a statistics class. For the latter, we are given z-tables for some of our tests. I don't like these z-tables. Thus, I decided that a more direct approach (fundamental theorem of calculus) would be more accurate and, more importantly, more fun. My...

Can someone explain to me how one gets the values of n, l, and ml (principle quantum number, azimuthal quantum number, magnetic quantum number, respectively) from the Schrodinger equation for use in chemistry involving distribution of electrons in a hydrogen atom?

In Griffiths, for deriving the bound charges for a given polarization P , the formula used is the general formula for dipoles .i.e ( equation 4.9) {Here the potential at r is calculated due to the dipole at r' ) V(r) = ∫\frac{x.P(r')}{X^2}d\tau' Here X = r - r' , and x = unit vector in...

Hello guys, I'm studying Thermodynamics and I don't totally see how you introduce the potencials using Legendre transformations. I have seen a non formal explanation showing how you can interpret them, but not a rigorous demonstration of how you get them via the Legendre transformations...

Hello Everybody, Carroll introduces in page 106 of his book "Spacetime and Geometry" the variational method to derive the geodesic equation. I have a couple of questions regarding his derivation. First, he writes:" it makes things easier to specify the parameter to be the proper time τ...

Homework Statement I've searched everywhere, and I cannot find an example of calculation of Lie derivation of a metric. If I have some vector field \alpha, and a metric g, a lie derivative is (by definition, if I understood it): \mathcal{L}_\alpha g=\nabla_\mu \alpha_\nu+\nabla_\nu...