Question

A(r)=Aexp(-(x^2+y^2)/ro^2)exp(-jkz) The wave function representation a true valid wave solution of Helmholtz equation?

A(r)=Aexp(-(x^2+y^2)/ro^2)exp(-jkz) The wave function representation a true valid wave solution of Helmholtz equation?

Science   Advanced-Physics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Helmholtz equation is:

where A is given function and m is its eigen value

Laplacian operator we define on a function as :

Given

Put

where m is its eigen value

Hence where

Hence A satisfies Helmholtz equation

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Is the following a valid probability density function? f(x) = c*exp(-(max(1,x^2)) (for all values of x...
Is the following a valid probability density function? f(x) = c*exp(-(max(1,x^2)) (for all values of x in the Real plane) If not, for what value of c (c = constant) this function will be a valid PDF?
1252) y=(C1)exp(Ax)+(C2)exp(Bx)+F+Gx is the general solution of the second order linear differential equation: (y'') + (...
1252) y=(C1)exp(Ax)+(C2)exp(Bx)+F+Gx is the general solution of the second order linear differential equation: (y'') + ( -4y') + ( 3y) = ( 2) + ( -7)x. Find A,B,F,G, where A>B.
Let y be the solution of the equation a) y ′ = 2 x y, satisfying...
Let y be the solution of the equation a) y ′ = 2 x y, satisfying the condition y ( 0 ) = 1. Find the value of the function f ( x ) = ln ⁡ ( y ( x ) ) at the point x = 2. b) Let y be the solution of the equation y ′ = sqrt(1 − y^2) satisfying the condition  y ( 0 ) = 0. Find the value of the function  f ( x...
A standing wave’s function is y(x,t) = Asin(kx)cos(?t). Prove that this equation is indeed a solution...
A standing wave’s function is y(x,t) = Asin(kx)cos(?t). Prove that this equation is indeed a solution to the wave equation.
1252) y=(C1)exp(Ax)+(C2)exp(Bx)+F+Gx is the general solution of the second order linear differential equation: (y'') + (...
1252) y=(C1)exp(Ax)+(C2)exp(Bx)+F+Gx is the general solution of the second order linear differential equation: (y'') + ( -9y') + ( 20y) = ( -9) + ( -8)x. Find A,B,F,G, where A>B. This exercise may show "+ (-#)" which should be enterered into the calculator as "-#", and not "+-#". ans:4
a)is the function f (x) = x exp ^(-x ^ 2/2) a proper function of the...
a)is the function f (x) = x exp ^(-x ^ 2/2) a proper function of the operator d2 / dx2-x2? if so, what is the intrinsic value? b)is the function f (x) = exp (4ix) +exp (-4ix) its own function of the operator d2 / dx2? if so, what is the intrinsic value?
Verify that the function y=x^2+c/x^2 is a solution of the differential equation xy′+2y=4x^2, (x>0). b) Find...
Verify that the function y=x^2+c/x^2 is a solution of the differential equation xy′+2y=4x^2, (x>0). b) Find the value of c for which the solution satisfies the initial condition y(4)=3. c=
a) Let y be the solution of the equation y ′ − [(3x^2*y)/(1+x^3)]=1+x^3 satisfying the condition  y...
a) Let y be the solution of the equation y ′ − [(3x^2*y)/(1+x^3)]=1+x^3 satisfying the condition  y ( 0 ) = 1. Find y ( 1 ). b) Let y be the solution of the equation y ′ = 4 − 2 x y satisfying the condition y ( 0 ) = 0. Use Euler's method with the horizontal step size  h = 1/2 to find an approximation to the value of the function y at x = 1. c) Let y...
Show that the function describing a wave, D(x,t) = (3.00/(2.00x - t)^2 + 1.00) is a...
Show that the function describing a wave, D(x,t) = (3.00/(2.00x - t)^2 + 1.00) is a solution of the linear wave equation. Determine the wave speed.
Verify that the function in the following question is the solution of wave equation w=f(u), where...
Verify that the function in the following question is the solution of wave equation w=f(u), where f is a differentiable function of u, and u = a(x+ct), where a is a constant
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT