Use equation (5.13) and the Fourier integral representation of to write a solution of the problem on the real line:
Also reformulate the solution using equation (5.18).
Problem:
Equation (5.13):
Equation (5.18):
Use equation (5.13) and the Fourier integral representation of to write a solution of the problem...
Consider a potential well, whose potential is given by (a) Evaluate the reflection and transmission coefficient for the case E > 0. (b) Use your result for the transmission coefficient obtained in (a) above, to evaluate the transmission coefficient for the potential barrier, (V0 > 0) for the case E < V0. Please show all steps thoroughly S-V, (-a <r <a) 10, elsewhere JV, (-a <r <a) V.C) = 0. elsewhere
There are 30 people that donated to a church. The amount each person donated has probability density function Find out the probability that exactly 5 people donated between 20 and 30. ,(1)-(*(50-r), (50-x), ifo ifo < x < 50 otherwise TA
Let be the distribution function defined by Let be the Lebesgue-Stieltjes measure asociated to . Determine the measurements of the fpllowing sets: We were unable to transcribe this imageF(x) = 0 if 1+r if 2+x? if 19 if I <-1 -1 <r <0 0<r<2 > 2 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image(-1, 0]υ (1,2) 10, ) U (1, 2 (1 :...
The amount of kerosene, in thousands of litres, in a tank at the beginning of any day is a random amount Y from which a random amount X is sold during that day. Suppose that the tank is not resupplied during the day so that x y, and assume that the joint density function of these of these variables is Determine the correlation coefficient between X and Y and interpret the value calculated. We were unable to transcribe this imagef...
Give algorithms for generating random variables from the following distributions. b. 1-2 if 0<<1
Using the result of exercise 7(see question 7 below), give algorithms for generating random variables from the following distributions. b. 1-2 if 0<<1 7. (The Composition Method) Suppose it is relatively easy to generate random variables from any of the distributions F,,-I, . . . , n. How could we generate a random variable having the distribution function 12 i-1 where p,, -1.... . n, are nonnegative numbers whose sum is 1?
(4) (a) Compute the Fourier series for the function f(s)-- interval [-T, on the (b) Compute the solution u(t,a) for the partial differential equation on the interval [o, ) luWith u(t, 0) u(t,1)-0 for t>0 (boundary conditions) u(o,z)-3 sin(2x)-5 sin(5z) + sin(6z), for O < < 1 (initial conditions) (20 points) (4) (a) Compute the Fourier series for the function f(s)-- interval [-T, on the (b) Compute the solution u(t,a) for the partial differential equation on the interval [o, )...
(4) (a) Compute the Fourier series for the function f(x) interval [-π, π]. 1-z on the (b) Compute the solution u(t, z) for the partial differential equation on the interval [0, T): 16ut = uzz with u(t, 0)-u(t, 1) 0 for t>0 (boundary conditions) (0,) 3 sin(2a) 5 sin(5x) +sin(6x). for 0 K <1 (initial conditions) (20 points) Remember to show your work. Good luck. (4) (a) Compute the Fourier series for the function f(x) interval [-π, π]. 1-z on...