1. ### S-wave phase shift for quantum mechanical scattering

a.) The potential is a delta function, so ##V \left( r \right) = \frac {\hbar^2} {2\mu} \gamma \delta \left(r-a \right)##, therefore ##V \left( r \right) = \frac {\hbar^2} {2\mu} \gamma ## at ##r=a##, and ##V \left( r \right) = 0## otherwise. I've tried a few different approaches: 1.) In...
2. ### Problem with the Finite Element Method applied to Electrostatics

Hi! I have a code that solve the poisson equation for FEM in temperature problems. I tested the code for temperature problems and it works! Now i have to solve an Electrostatic problem. There is the mesh of my problem (img 01). At the left side of the mesh we have V=0 (potencial). There is a...
3. ### I Is the derivative of a discontinuity a delta function?

In these notes, https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016/lecture-notes/MIT8_04S16_LecNotes10.pdf, at the end of page 4, it is mentioned: (3) V(x) contains delta functions. In this case ψ'' also contains delta functions: it is proportional to the product of a...
4. ### Recovering the delta function with sin⁡(nx)/x

Homework Statement Ultimately, I would like a expression that is the result of an integral with the sin(nx)/x function, with extra terms from the expansion. This expression would then reconstruct the delta function behaviour as n goes to infty, with the extra terms decaying to zero. I...
5. ### 2D Integrating With Quadratic Arg. of Delta Function

Homework Statement I have a 2D integral that contains a delta function: ##\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\exp{-((x_2-x_1)^2)+(a x_2^2+b x_1^2-c x_2+d x_1+e))}\delta(p x_1^2-q x_2^2) dx_1 dx_2##, where ##x_1## and ##x_2## are variables, and a,b,c,d,e,p and q are some real...
6. ### A Inverse Laplace transform of F(s)=exp(-as) as delta(t-a)

This is mostly a procedural question regarding how to evaluate a Bromwich integral in a case that should be simple. I'm looking at determining the inverse Laplace transform of a simple exponential F(s)=exp(-as), a>0. It is known that in this case f(t) = delta(t-a). Using the Bromwich formula...
7. ### I Square root of the delta function

Is square root of delta function a delta function again? $$\int_{-\infty}^\infty f(x) \sqrt{\delta(x-a)} dx$$ How is this integral evaluated?
8. ### Finding the Delta Function of a Thin Ring

Homework Statement [/B] A very thin plastic ring (radius R) has a constant linear charge density, and total charge Q. The ring spins at angular velocity \omega about its center (which is the origin). What is the current I, in terms of given quantities? What is the volume current density J in...
9. ### A Divergence of 1/r^n...n>0

I have read in Griffiths electrodynamics that divergence of 1/r^2 is delta function and I thought it was the only special case...I have understood the logic there.... but a question came in mind...what would happen in general if the function is 1/r^n ....where n is positive integer>0.....because...
10. ### How to make a delta function signal in a circuit?

Basically I want to test my analog circuit using a forcing function that has a form of a delta function. The function generator I use outputs sine wave, triangular wave and square wave (+ve and -ve output in one period). Are there any ways to produce a square wave that has an output for like 5%...
11. ### Integral of sin and cos

Starting from FT relation of delta function, I can write the followings: $$\int_{-\infty}^{\infty} \cos{\alpha x} dx = 0$$ $$\int_{-\infty}^{\infty} \sin{\alpha x} dx = 0$$ The question is how am I supposed to prove those equations, sin and cos are stable oscillating functions.
12. ### Integrating a delta function with a spherical volume integral

Homework Statement Integrate $$\int_V \delta^3(\vec r)~ d\tau$$ over all of space by using V as a sphere of radius r centered at the origin, by having r go to infinity. Homework Equations The Attempt at a Solution This integral actually came up in a homework problem for my E&M class and...