# What is Neumann: Definition and 97 Discussions

Neumann is German for "new man", and one of the 20 most common German surnames.

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1. ### A Solve the homogenous Neumann problem

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...
2. ### Other New Bio "The Man from the Future" by Ananyo Bhattacharya

The Man from the Future by Ananyo Bhattacharya (it’s out in Britain, not until Feb. in US) Anybody have any thoughts on it?
3. ### Koopman–von Neumann mechanics references

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...
4. ### Solve this PDE with Neumann boundary conditions

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...
5. ### I Did von Neumann coin the eth or dyet for the inexact differential?

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...
6. ### Von Neumann Entropy time derivative(evolution)

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))
7. ### I Von Neumann entropy for "similar" pvm observables

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...
8. ### A Dirichlet and Neumann boundary conditions in cylindrical waveguides

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...
9. ### Did John von Neumann ever go to Oslo or any other part of Norway?

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...
10. ### I How does the von Neumann equation relate to Schrödinger's equation?

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...
11. ### I Verification regarding Neumann conditions at time derivative

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...
12. ### Derivative of a term within a sum

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...
13. M

### Mathematica Why is the Neumann boundary condition not satisfied in this FEA simulation?

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...
14. M

### Mathematica 2D PDE Solution with Neumann BC: Plot Comparison

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...
15. ### Mathematical Biology- Neumann BCs, Turing Analysis

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 ##...
16. ### A Von Neumann Entropy of a joint state

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...
17. ### Green's Function with Neumann Boundary Conditions

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...
18. ### I Povm's and Von Neumann Meaurements

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...
19. ### I Von Neumann measurement scheme

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...
20. ### I Rényi entropy becomes von Neumann entropy

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!
21. ### Definition and alternatives for Von Neumann architecture?

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...
22. ### A Where does Von Neumann say that consciousness causes collapse

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...
23. ### I Poisson Equation Neumann boundaries singularity

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...
24. ### I Chladni plate with Neumann conditions

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...
25. ### A Neumann boundary conditions in calculus of variations

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
26. ### Utility function von Neumann Morgenstern

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...
27. ### Maximum value of Von Neumann Entropy

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 =...
28. ### PDE: Wave Equation with Neumann conditions

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...
29. ### A Laplace equation on a trapezoid

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.
30. ### Q about Poisson eqn w/ Neumann boundary conditions as in Jackson

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...
31. ### Is a Von Neumann Universe possible in ZC without the Axiom of Choice?

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
32. ### Von Neumann QM Rules Equivalent to Bohm?

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...
33. ### About von Neumann density

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
34. ### MHB Applying Neumann Boundary Conditions in 1D

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...
35. ### Proof of "Entropy of preparation" in Von Neumann entropy

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}...
36. ### Mathematical Game Theory (Von Neumann Morganstern Utility)

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...
37. ### Von Neumann Analysis: Refresh Numerical Science | Any Help Appreciated

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...
38. ### Concerning spherical Bessel and Neumann functions

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...
39. ### Maple Heat equation with Neumann B.C. in Maple

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...
40. ### How to compute Von Neumann entropy?

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...
41. ### Alternative to Von Neumann bias correction method

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...
42. ### Neumann and Dirichlet BCs in discrete Poisson EQ

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...
43. ### Problem with solution of a PDE, Neumann functions

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...
44. ### A Bessel's functions of the second kind (Neumann' functions) deduction

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...
45. ### Backward euler method for heat equation with neumann b.c.

I am trying to solve the following pde numerically using backward f.d. for time and central di fference 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...
46. ### How to set up Neumann boundary condition for a PDE in a coordinate-invariant form?

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...
47. ### Neumann Boundary Conditions using FTCS on the Heat Equation

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...
48. ### Wave equation with nonhomogenous neumann BC

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...
49. ### Deducing the solution of the von Neumann equation

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}]...
50. ### What is going on here? (Heat equation w/ Neumann conditions)

Homework Statement Solve the heat equation ut=uxx on the interval 0 < x < 1 with no-flux boundary conditions. Use the initial condition u(x,0)=cos ∏x Homework Equations We eventually get u(x,t)= B0 + ƩBncos(n∏x/L)exp(-n2∏2σ2t/L2) where L=1 and σ=1 in our case. B0 is...