Derivation Definition and 1000 Threads

Hi all, Is it possible to derive the equation p = ymv, and hence based on this, kinetic energy formula, without referring to 4-vectors or 2-dimensional collisions, that is derive it in one dimension? I tried this website/pdf but the mathematics is beyond my understanding. So could some one...

(The problem I have is really at the end, however, I have provided my whole argument in detail for clarity and completeness at the cost of perhaps making the thread very unappealing to read) Homework Statement (c.f Di Francesco's book, P.41) We are given that the transformed action under an...

I am self studying the 17th Chapter of "Mathematical Methods for Physics and Engineering", Riley, Hobson, Bence, 3rd Edition. It is about eigenfunction methods for the solution of linear ODEs. Homework Statement On page 563, it states: "As noted earlier, the eigenfunctions of a...

Is there anywhere I can see the explicit derivation for a massless real scalar and for the EM field? thank you.

The derivation of Planck's law in my textbook begins with the assumption that the energy of an oscillator with frequency ##\nu## is quantised in units of ##h\nu##. It follows that the average energy of such an oscillator (in equilibrium with a reservoir at temperature ##T##) will be...

I'm studying classical mechanics and I'm stumbling in the quantity of differential identities. Being S the action, H the hamiltonian, L the lagrangian, T the kinetic energy and V the potential energy, following the relationships: But, the big question is: that's all? Or has exist more...

Hi, I'm looking at a derivation of the thermodynamics of black-body radiation. My question is in regards to the math of the derivation. Using the first law of thermodynamics and considering an adiabatic expansion of the cavity, it can be stated that dU = -\frac{u}{3}dV Here small u...

Hi all, Here is the derivation of kinetic energy from Work: W = ∫Fds From the second law of motion F = dp/dt, which is equal to mdv/dt, so: W = m∫dvdx/dt which = m∫dv x v because dx/dt = v Therefore W = 1/2mv2, when integrated. However from simple algebra derivation, W = Δ1/2mv2...

Hi, The attachment below is about strain rate in fluids*. It shows how the strain rate d\phi/dt is related to the velocity field derivative du/dx when you stretch the element in x (i.e. longitudinal strain). It has no intermediate steps, and I can't see how the angle has been related to...

All the derivations of the Rayleigh-Jeans 'Law' I've seen assume that the electromagnetic radiation is enclosed in a cube. I'm trying to derive the law using less arbitrary circumstances. That is, by starting with the equation U=\int \left[ \frac{\epsilon_0}{2}E^2 + \frac{1}{2\mu_0}B^2...

http://quantumfreak.com/derivation-of-pvnrt-the-equation-of-ideal-gas/ here is the link. so we assume the particle hits two surfaces of the cube, thus pressure is 1/3. combine the equation #11 and #12 we solve kinetic energy equation #12 for mv2. 13...

I want to consider the rate at which time slows as gravity increases near a massive object such as a sun or even a black hole. Obviously there is a distance component here but I am after a generalisation that simply shows the relationship between time and gravity (ought to be possible)...

Hi folks, Been trying to fill some of the more formal gaps in my knowledge by tackling the more technical stuff in P&S Chapter 7. Their derivation of the LSZ formula is quite different to those of books like, say, Srednicki, as they basically Fourier transform the whole argument as I...

So I'm not OK with how some people derive this equation. These people consider a pipe whose endings have cross-sectional areas and heights which are different. They then use the conservation of energy principle by saying dW = dK + dU (Where W is work, K is kinetic energy, and U is potential...

Hiya can anyone show how to derive the euqation of damped frequency for a spring ωd = ωnsqrt(1-ζ2)

Hi everybody! First post!(atleast in years and years). The stationary KdV equation given by $$ 6u(x)u_{x} - u_{xxx} = 0 $$. It has a solution given by $$ \bar{u}(x)=-2\sech^{2}(x) + \frac{2}{3} $$ This solution obeys the indentity $$ \int_{0}^{z}\left(\bar{u}(y) -...

I'm currently reading about thermodynamics and osmosis and I happened to stumble across this paper. There is one thing I don't really understand, though.. In chapter 8 the author wishes to give a thermodynamic explanation of the osmotic pressure so I've been reading through the derivation. When...

In the semi-classical treatment of the ideal gas, we write the partition function for the system as $$Z = \frac{Z(1)^N}{N!}$$ where ##Z(1)## is the single particle partition function and ##N## is the number of particles. It is semi-classical in the sense that we consider the...

Whilst reading following a derivation of the Relativistic Energy equation I came across the following: d/dt[mu/(1-u2/c2)1/2] = [m/(1-u2/c2)3/2] du/dt. I was wondering how that step was done.

Hi, I am working through Section 5.8 of Sean Carroll's book on GR. Does someone know where I can find the bridging steps that take me from \nabla_\mu T^{\mu\nu} = 0 to (\rho + p)\frac{d\alpha}{dr} = -\frac{dp}{dr} This is equation 5.153, and when I try to derive it through the...

I am trying to follow a Maxwell's equations derivation for light scattering but don't understand 'why' the authors do the steps they do at this start bit. Help would be greatly appreciated... It starts with the incident electric field equation. \textbf{E}_{0}(\textbf{r},t) = \textbf{E}_0...

Dear , Can someone please tell me what material I can refer to for the derivation of Marcus Electron Transfer Theory.

Dear , Can someone please tell me what material I can refer to for the derivation of Marcus Electron Transfer Theory.

Reading into some special relativity, I have seen E=mc^2 proposed from the assumption of four momentum conservation and the fact that the 'mass' component varies with velocity with the gamma factor, like a kinetic energy. This seems a bit of a leap of faith to me so I was wondering if there...

Is the following approach used for the derivation of the ideal gas equation correct? Here's the link: http://www.mikeblaber.org/oldwine/chm1045/notes/Gases/IdealGas/Gases04.htm

can you check if my solution here is correct. If not can you tell me how to do it properly. thanks!

This is my first time posting here, I apologize if this is the wrong place to ask such a question. In my book I have the following London equation written (1st) for a superconductor: E=μ0λ2L∂J/∂t where: λ2L is the london penetration depth. My understanding is that it can be derived...

Okay, so the job I need to do is derive an equation for the radius of an object in terms of its frequency. These are the equations that we are allowed to use: v(Linear velocity) = rω v=2πr/T ω (angular velocity)=2πf f (frequency)= 1/T (time period) T= 2πr/v a (centripetal...

I'm going to run through a derivation I've seen and ask a few questions about some parts that I'm unsure about. Firstly the theorem: For every symmetry of the Lagrangian there is a conserved quantity. Assume we have a Lagrangian L invariant under the coordinate transformation qi→qi+εKi(q)...

Last semester I had intermediate mechanics, and we spent a good amount of the class studying the LaGrangian. One thing that I never got an explanation for was why ##L = T-V##, as opposed to ##T+V##. The only reason I can think of is the "give and take" relationship that Kinetic and Potential...

This picture from https://www.amazon.com/dp/0198534469/?tag=pfamazon01-20 is all you need to derive the Cauchy-Riemann equations, i.e. from the picture we see i \frac{\partial f}{\partial x} = \frac{\partial f}{\partial y} should hold so we have i \frac{\partial f}{\partial x} = i...

I'm currently going through my courses notes for relativity. We looked at Einsteins two postulates and then said that time must therefore dilate due to constant speed of light. That I understand, however I'm still confused about the Lorentz's transformations. My notes start with a basic form of...

Homework Statement The start of the derivation is shown in the attached image. I don't follow the argument that takes us from (91) to (92). The Attempt at a Solution I accept that the wavefunction of (91) is not an eigenstate of the Hamiltonian. I'm not clear where equation (92) came...

hey pf! so i have a small question when deriving the navier-stokes equations from Newton's 2nd law. specifically, Newton states that $$\Sigma \vec{F} = m \vec{a} = m \frac{d \vec{v}}{dt}$$ when setting a control volume of fluid and dealing with the time rate-of-change of momentum we write...

When deriving telegrapher's equations using Kirchhoff current/voltage laws (this equivalent circuit), are the shunt capacitance and shunt conductance in parallel? I assume not, and if not, are they in parallel with the voltages at each corresponding end? I am confused by this; in Pozar's...

Homework Statement Hi, If there is a series combination of a resistor and an initially charged capacitor, I know that the decay of the voltage is given by the equation v(t) = Ae^(-t/RC) where V(0) = A = V0. But i am unsure of how to get to this equations. Homework Equations If I assume...

Below is part of derivation of the Boltzmann equation in an electric and magnetic field. I don't understand how to arrive at the bottom equation though. It is known that the dependence of the original distribution function is the given. My idea is to use chain rule but I don't see how to get a...

I am not sure if I should be posting this under QM or under Linear Algebra, since it appears to be an algebraic step that I do not see, and am asking the wonderful people on this forum to spell it out for me. In John Baez's derivation of the Energy-time Uncertainty relation...

This is not exactly a homework question. In a physics textbook, they derive an expression for gravitational redshift of a photon emitted by a star at a large distance from the source by taking photon as a mass traveling up, against a gravitational potential and hence expending its...

In Schutz, the christofell symbols are dervied from applying the product rule to a vector in a curvillinear basis. In Wald, the christofell symbols are dervied by making an ansatz of the form a covariant derivative must take and then imposing conditions on it like the metric covariant...

Homework Statement find the derivative of the given function: f(x)= 6 - (1/x) / x-2 Homework Equations The Attempt at a Solution the solution on the answer key is (-6x^2 + 2x - 2 ) / (x^2 (x-2)^2) i don't know how to solve it :(

I was wondering if somebody could clear up some confusion I have regarding this. I've been going over the derivation for obtaining the integrating factor again in my book and there is one step I don't understand. There's no point going through the whole thing from scratch, but I've got to...

Has anyone seen the derivation of \(\ddot{\mathbf{r}} = -\frac{\mu}{r^3}\mathbf{r}\) into state matrix form? If so, can they provide a link?

Homework Statement Problem statement is in the attachment HW 5, it is problem #1. Homework Equations The Attempt at a Solution I am just stuck with a whole bunch of variables and this just looks like a complete mess

Homework Statement Consider a set of data points: (x1, y1), (x2,y2). One seeks to find the best coefficients A and B such that the sum of squared vertical distances of the data f(x) = Ax + B is minimized. Let D = ∑[yi - f(xi]2. By requiring the derivatives of D respect to both A and B each to...

I know how to derive the lorentz time dilation equation. I am wondering how to derive the equation for gravitational time dilation: T=To(1/(sqrt(1-(2GM)/(Rc2)))

Homework Statement First off, this is NOT a homework problem. This is a conceptual question I have regarding the derivation of the drift velocity v_d =[(qE)/m] \tau Typically, when this formula is derived, you first calculate the acceleration of a particle in the electric field (qE/m) and...

Every time I try to read Peskin & Schroeder I run into a brick wall on page 15 (section 2.2) when they quickly derive the Euler-Lagrange Equations in classical field theory. The relevant step is this: \frac{∂L}{∂(∂_{μ}\phi)} δ(∂_{μ}\phi) = -∂_{μ}( \frac{∂L}{∂(∂_{μ}\phi)}) δ(\phi) + ∂_{μ}...

Every time I try to read Peskin & Schroeder I run into a brick wall on page 15 (section 2.2) when they quickly derive the Euler-Lagrange Equations in classical field theory. The relevant step is this: \frac{∂L}{∂(∂_{μ}\phi)} δ(∂_{μ}\phi) = -∂_{μ}( \frac{∂L}{∂(∂_{μ}\phi)}) δ(\phi) + ∂_{μ}...

In page 30 of book "An introduction to quantum field theory" by Peskin and Schroeder in the derivation of Klein-Gordon propagator, why p^0=-E_p in the second step in equation (2.54). and why change "ip(x-y)" to "-ip(x-y)"? I thought a lot time, but get no idea. Thank you for your giving me an...