# laplacian

1. ### A The Laplacian of the potential q*exp(-r)/r

Hello, I have a problem where I'm supposed to calculate the charge distribution ρ. I need to calculate it by applying the Laplacian operator to the potential Θ. The potential is the function: q*exp(-αr)/r I found on the internet that for this type of potentials I cannot just apply the...
2. ### A Replacing a non-harmonic function with a harmonic function

I am solving a problem of the boundary condition of Dirichlet type, in order to solve the problem, the functions within the differential equations suppose to be harmonic. I have a function f(x,y,z) (the function attached) which is not harmonic. I must find an equivalent function g(x,y,z) which...
3. ### Divergence operator for multi-dimensional neutron diffusion

1. Homework Statement [1] is the one-speed steady-state neutron diffusion equation, where D is the diffusion coefficient, Φ is the neutron flux, Σa is the neutron absorption cross-section, and S is an external neutron source. Solving this equation using a 'homogeneous' material allows D to be...
4. ### Laplacian in spherical coordinates

1. Homework Statement Hello at all! I have to calculate total energy for a nucleons system by equation: $E_{tot}=\frac{1}{2}\sum_j(t_{jj}+\epsilon_j)$ with $\epsilon_j$ eigenvalues and: $t_{jj}=\int \psi_j^*(\frac{\hbar^2}{2m}\triangledown^2)\psi_j dr$ My question is: if I'm in...
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### I What is the gradient in polar coordinates?

Hi, on this page: https://en.wikipedia.org/wiki/Laplace_operator#Two_dimensions the Laplacian is given for polar coordinates, however this is only for the second order derivative, also described as \delta f . Can someone point me to how to represent the first-order Laplacian operator in polar...
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### I Laplacian Operator in 2D

Hi, I have that the Laplacian operator for three dimensions of two orders, \nabla ^2 is: 1/r* d^2/dr^2 (r) + 1/r^2( 1/sin phi d/d phi sin phi d/d phi + 1/sin^2 phi * d^2/d theta^2) Can this operator be used for a radial system, where r and phi are still valid, but theta absent, by setting...
7. ### 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...
8. ### I Question about solution to Laplacian in Spherical Polars

I was following this derivation of the solution to the Laplacian in spherical polars. I was wondering where the two equations $\lambda_{1} + \lambda_{2} = -1$ and $\lambda_{1}\lambda_{2} = -\lambda$ come from? Thanks.
9. ### Question about a boundary-value problem (electrostatics)

Laplacian for polars: $$\frac{1}{r}\frac{\partial}{\partial r}\left( r\frac{\partial \phi}{\partial r}\right) + \frac{1}{r^{2}}\frac{\partial^{2} \phi}{\partial \theta^{2}} = 0$$ This is in relation to a problem relating to a potential determined by the presence of a wedge shaped metallic...
10. ### Trouble understanding $g^{jk}\Gamma^{i}{}_{jk}$

Hi friends, I'm learning Riemannian geometry. I'm in trouble with understanding the meaning of $g^{jk}\Gamma^{i}{}_{jk}$. I know it is a contracting relation on the Christoffel symbols and one can show that $g^{jk}\Gamma^i{}_{jk}=\frac{-1}{\sqrt{g}}\partial_j(\sqrt{g}g^{ij})$ using the...
11. ### Integrate Laplacian operator by parts

This is the key step to transform from position space Schrodinger equation to its counterpart in momentum space. How is the first equation transformed into 3.21? To be more specific, how to integral Laplacian term by parts?
12. ### Delta Function Identity in Modern Electrodynamics, Zangwill

I am currently reading Modern Electrodynamics by Andrew Zangwill and came across a section listing some delta function identities (Section 1.5.5 page 15 equation 1.122 for those interested), and there is one identity that really confused me. He states: \begin{align*} \frac{\partial}{\partial...
13. ### Obtain the magnetic field from this experimental setup?

1. Homework Statement Hi all, I would appreciate some help with the following problem; I need to obtain and visualize the current flow and magnetic field profile of an elliptic cylinder (made from ferromagnetic material) which has a left section set at 0 volts and a right section set at 5...
14. ### How to get the laplacian of a scalar field?

Hi, I am trying to calculate the laplacian of a scalar field but I might actually need something else. So basically I am applying reaction diffusion on a 2d image. I am reading the neighbours, multiplying them with these weights and then add them. This works great. I don't know if what I am...
15. ### Poisson Summation in Heat Equation (Polar Coordinates)

1. Homework Statement I'm currently trying to follow a derivation done by Shankar in his "Basic Training in Mathematics" textbook. The derivation is on pages 343-344 and it is based on the solution to the two dimensional heat equation in polar coordinates, and I'm not sure how he gets from one...