Neumann Definition and 98 Threads

Suppose I have a boundary condition f'(0)=a. I know the value of f(x) at x=h/2,3h/2. Does it make sense to write: f'(x)=af(x)+bf(x+h/2)+cf(x+3h/2) Using Taylor series to expand, we obtain the following: f'(x)=(a+b+c)f(x)+\frac{h}{2}(b+3c)f'(x)+\frac{h^{2}}{8}(b+9c)f''(x) By equating...

I am going through this notes and i would like some clarity on the highlighted part...the earlier steps are pretty easy to follow... Is there a mistake here...did the author mean taking partial derivative with respect to ##t##? is ##\dfrac{d}{dt}## a mistake? How did that change to next line...

The Man from the Future by Ananyo Bhattacharya (it’s out in Britain, not until Feb. in US) Anybody have any thoughts on it?

Hello everyone, I am new here. I am studying physics as a self-taught student. I have been studying classical Lagrangian and Hamiltonian mechanics from Goldstein's book and have read that there is an additional formulation of classical mechanics in Hilbert spaces. Is it worth studying? Do you...

Hi all, I was hoping someone could check whether I computed part (4) correctly, where i find the solution u(t,x) using dAlembert's formula: $$\boxed{\tilde{u}(t,x)=\frac{1}{2}\Big[\tilde{g}(x+t)+\tilde{g}(x-t)\Big]+\frac{1}{2}\int^{x+t}_{x-t}\tilde{h}(y)dy}$$ Does the graph of the solution look...

Today the inexact differential is usually denoted with δ, but in a text by a Russian author I found a dyet (D-with stroke, crossed-D) instead: In response to my question to the author about this deviation from normal usage, he stated that this was a suggestion from von Neumann. (Which of course...

I'm not sure about my proof. So please check my step. I used log as a natural log(ln). Specially, I'm not sure about "d/dt=dρ/dt d/dρ=i/ħ [ρ, H] d/dρ" in the second line. and matrix can differentiate the other matrix? (d/dρ (dρ lnρ))

The von Neumann entropy for an observable can be written ##s=-\sum\lambda\log\lambda##, where the ##\lambda##'s are its eigenvalues. So suppose you have two different pvm observables, say ##A## and ##B##, that both represent the same resolution of the identity, but simply have different...

The book of Balanis solves the field patterns from the potential functions. Let say for TE modes, it is: F_z(\rho, \phi, z) = A_{mn} J_m(\beta_{\rho}\rho) [C_2 \cos(m\phi) + D_2 \sin(m\phi)] e^{-j\beta_z z} There is no mention of how to solve for the constant A_{mn} . Then, from a paper...

I do not know exactly where to ask this. I do not even know if I can. I chose the General Discussion forum since it seems to me the best place to ask this within this site. Having said this, Did John von Neumann ever go to Oslo or any other part of Norway? It is known that he traveled at least...

I was trying to show how to get Schrödinger’s equation from the von Neumann equation and I’m not quite confident enough in my grasp of the functional analysis formalism to believe my own explanation. Starting from $$i\hbar\frac{\partial}{\partial t}\rho=[H,\rho]$$ We have...

Hi, just a question regarding neumann conditions, I seem to have forgotten these things already. I think this question is answerable by a yes or a no. So given the 2D heat equation, If I assign a neumann condition at say, x = 0; Does it still follow that at the derivative of t, the...

Homework Statement [/B] From the Rodrigues’ formulae, I want to derive nature of the spherical Bessel and Neumann functions at small values of p. Homework Equations [/B] I'm going to post an image of the Bessel function where we're using a Taylor expansion, which I'm happy with and is as far...

Hi PF! I am solving ##\nabla^2\phi = 0## in Mathematica via NDSolveValue. Rather than waste your time explaining the 2D domain ##\Omega##, check out the code at the bottom of page (copy-paste into Mathematica). Specifically, I am enforcing a Neumann BC on the curved boundary ##\Gamma## through...

Hi PF! I'm solving a 2D PDE using NDSolveValueMesh. On one boundary I apply a Neumann BC. Attached are two plots: the top is the boundary condition and the functional value. Notice both are exactly the same. However, the lower plot shows a directional derivative evaluated on the same boundary...

This is probably a stupid question but I have Neumann BC boundary : ## \nabla u . \vec{n} =0## (same for ##v##)conditions for the following reaction-diffusion system on a [0,L_1]x[0,L_2]x...x...[0,L_n] n times in n dimensional space so ##u=u(x_1,...,x_n,t)## is a scalar I believe? so that ##...

Definition 1 The von Neumann entropy of a density matrix is given by $$S(\rho) := - Tr[\rho ln \rho] = H[\lambda (\rho)] $$ where ##H[\lambda (\rho)]## is the Shannon entropy of the set of probabilities ##\lambda (\rho)## (which are eigenvalues of the density operator ##\rho##). Definition 2 If...

Homework Statement [/B] Determine the Green's functions for the two-point boundary value problem u''(x) = f(x) on 0 < x < 1 with a Neumann boundary condition at x = 0 and a Dirichlet condition at x = 1, i.e, find the function G(x; x) solving u''(x) = delta(x - xbar) (the Dirac delta...

Hi All Read a thread that about Von-Neumann observations that was closed because it was a bit too vague, but I sort of got a sense of what the poster was on about - and it also is interesting anyway for anyone that doesn't know it so I thought I would do a post about it. Since Von-Neumann's...

I've been studying the von Neumann measurement scheme (and understanding the math part) where the system and apparatus are quantum in contrast to the orthodox where the apparatus is classical. I'd like to know the following. 1. Is the von Neumann measurement scheme 100% orthodox and believed by...

In holographic entanglement entropy notes like here, they let alpha go to one in (2.41) and get (2.42). But (2.41) goes towards infinity, when doing that! Can someone explain how alpha --> 1 will make (2.41) into (2.42)? Thank you!

I have been studying about computers and found that they evolved from the basic mechanical devices with limited functions to the amazing machines we have today. Its all very new and interesting to me. I believe that programming is the act of writing an algorithm in a higher or lower level...

It's often claimed that in Mathematical Foundations of Quantum Mechanics Von Neumann concluded that it's the observer's consciousness that collapses the wavefunction (Process 1). But I am reading Chapter 6 of the book (both original and translation) word by word, and I don't find this...

I am trying to solve the poisson equation with neumann BC's in a 2D cartesian geometry as part of a Navier-Stokes solver routine and was hoping for some help. I am using a fast Fourier transform in the x direction and a finite difference scheme in the y. This means the poisson equation becomes...

Hi there, I'm trying to simulate a vibrating plate with free edges. If i consider a consider a plate with fixed edges, the eigenvectors of the matrix bellow (which repesents the Laplacien operator) with S as a nxn tridiagonal matrix with -4 on the diagonal and 1s on either side (making the...

In calculus of variations, extremizing functionals is usually done with Dirichlet boundary conditions. But how will the calculations go on if Neumann boundary conditions are given? Can someone give a reference where this is discussed thoroughly? I searched but found nothing! Thanks

Homework Statement I have a financial intermediation model with delegated monitoring to a venture capitalist. At the moment all participants are risk neutral and i want to introduce risk aversion to the model. Therefore i need a utility function under the von neumann morgenstern criteria, ie...

Homework Statement Prove that the maximum value of the Von Neumann entropy for a completely random ensemble is ##ln(N)## for some population ##N## Homework Equations ##S = -Tr(ρ~lnρ)## ##<A> = Tr(ρA)## The Attempt at a Solution Using Lagrange multipliers and extremizing S Let ##~S =...

Homework Statement Consider the homogeneous Neumann conditions for the wave equation: U_tt = c^2*U_xx, for 0 < x < l U_x(0,t) = 0 = U_x(l, t) U(x,0) = f(x), U_t(x,0) = g(x) Using the separation of variables, find a nontrivial solution of (1). Homework Equations Separation of variables The...

Hello everybody! I know how to solve Laplace equation on a square or a rectangle. Is there any easy way to find an analytical solution of Laplace equation on a trapezoid (see picture). Thank you.

I am reading Jackson Electrodynamics (section 1.10 in 3rd edition) and he is discussing the Poisson eqn $$\nabla^2 \Phi = -\rho / \epsilon_0$$ defined on some finite volume V, the solution using Greens theorem is $$\Phi (x) = \frac{1}{4 \pi \epsilon_0} \int_V G(x,x') \rho(x')d^3x' +\frac{1}{4...

Why in ZC (ZFC-reemplacement+separation) can´t exist Von Neumann Universet not even till \omega2. Sorry, I am new in the forum and I dont´know use Latex

Bohm's deterministic theory was designed to be equivalent to standard QM, but what I'm not sure about is whether that includes Von Neumann's rules. Von Neumann's rules for the evolution of the wave function are roughly described by: Between measurements, the wave function evolves according to...

I want to ask if it is wrong to interpret the von Neumann density in a '' functional sense'' as a szego projector Hilbert spaces? thks

Hi, I've been doing some work on the finite element method. I have been able to calculate the stiffness matrix and load vector and apply both homogeneous and inhomogeneous Dirichlet conditions but am stuck on calculating the Neumann conditions. I have the definition of it as...

How should I prove this? From John Preskill's quantum computation & quantum information lecture notes(chapter 5) If a pure state is drawn randomly from the ensemble{|φx〉,px}, so that the density matrix is ρ = ∑px|φx〉<φx| Then, H(X)≥S(ρ) where H stands for Shannon entropy of probability {px}...

1: If u: omega---> reals is a Von Neumann Morganstern Utiliy function and L is a lottery, prove that expectation E is "linear" ie: E(Au(L)+B)=AEu(L)+B2. Given none:The Attempt at a Solution : My attempt at a solution has gone nowhere. I found a stanford and princeton game theory notes that went...

I'm trying to refresh some numerical science stuff. Von Neumann analysis, if I take a slimmed down equation, convection. \frac{∂u}{∂t}+a ∇ u =0 If I'm using Euler forward, \frac{u^{n+1}-u^n}{\Delta t}+\frac{a}{2h} \left( u_{j+1}^n -u_{j-1}^n \right) =0 For \hat{u}^n = G^n\hat{u}^0 a growth...

When transforming the Schrodinger equation into sphericall coordinates one usually substitutes psi(r,theta,phi) into the equation and ends up with something like this: -h(bar)^2/2m* d^2/dr^2*[rR(r)]+[V(r)+(l(l+1)*h(bar)^2)/2mr^2]*[rR(r)]=E[r R(r)] Question 1: How do I replace the Rnl(r) with...

Hello! I have written the code in Maple for Heat equation with Neumann B.C. Could anyone check it? I will be very grateful! Heat equation: diff(u(x,t),t)=diff(u(x,t),x,x); Initial condition: U(x,0)=2*x; Boundary conditions: Ux(0,t)=0; Ux(L,t)=0; I use centered difference approximation for...

I know how to get Von Neumann entropy from a density matrix. I want to get a real number from measurements that give real numbers as outcomes. (there are complex numbers in a density matrix). So suppose Charlie sends 1000 pairs of particles in the same state to Bob and Alice. They agree to...

Hi I have discovered that the Von Neumann bias correction method only works when the bias is 100% stable, for example tossing the same loaded coin again and again. Does anyone know of a bias correction method which can correct an unstable bias? Is this impossible? Edit: Let's say I have a...

Hello all. I am working on a problem and I am getting a bit confused. Suppose we have a poisson equation that we wish to solve subject to certain boundary conditions. Let's say we are in 1D (we can later extrapolate to more dimensions). Is it possible to impose Dirichlet boundary...

hello everyone i'm in my sixth semester of undergraduate physics and currently taking a math methods of physics class. So far we've been working with boundary value problems using PDE's. In the textbook we're using and from which I've been reading mostly (mathematical physics by eugene...

Homework Statement I need to obtain the Bessel functions of the second kind, from the expressions of the Bessel functions of the first kind. Homework Equations Laplace equation in circular cylindrical coordinates reads \nabla^2\phi(\rho,\varphi,z)=0 with...

I am trying to solve the following pde numerically using backward f.d. for time and central difference approximation for x, in MATLAB but i can't get correct results. \frac{\partial u}{\partial t}=\alpha\frac{\partial^{2}u}{\partial x^{2}},\qquad u(x,0)=f(x),\qquad u_{x}(0,t)=0,\qquad...

I'm having trouble finding out how to set up Neumann (or, rather, "Robin") boundary conditions for a diffusion-type PDE. More specifically, I have a scalar function f(\boldsymbol{x}, t) where \boldsymbol{x} is n-dimensional vector space with some boundary region defined by A(\boldsymbol{x})=0...

I am really confused with the concept of Neumann Boundary conditions. For the simple PDE ut=uxx for the domain from 0<=x<=1 I'm trying to use a ghost point (maintain a second order scheme) for the Neumann Boundary condition ux(0,t) = 0. I understand that I can setup a scheme to...

I've been searching online for the past week but can't seem to find what I am looking for. I need the analytic solution to the wave equation: utt - c^2*uxx = 0 with neumann boundary conditions that are not homogeneous, i.e. ux(0,t) = A, for nonzero A. also, the domain i require the...

Homework Statement \hat{\rho}(t)=? |\psi(t)\rangle=U(t,t_{0})|\psi(t_{0})\rangle \imath\hbar\partial_{t}\hat{p}=[\hat{H},\hat{\rho}] Homework Equations \imath\hbar\partial_{t}\hat{p}=[\hat{H},\hat{\rho}]...