• Problem 7. For a wave-function W.(x) = (2/a)" sin(x/a) calculate the average position (<x>). Is...
Problem 1. Wave function An electron is described by a wave function: for x < 0 *(z) = { ce Ce-s/1(1 – e-3/4) for x > 0 : where I is a constant length, and C is the normalization constant. 1. Find C. 2. Where an electron is most likely to be found; that is, for what value of x is the prob: bility for finding electron largest? 3. What is the average coordinate 7 of the electron? 4. What...
Explain ng on the particle as a function of x, for O <x < 7 meters?
2.33. Evaluate (x), (Px), A.x, APx, and Ax Apr for the normalized wave function { (x)= sin 0<x</ 0 elsewhere In the next chapter we will see that this wave function is the ground-state wave function for a particle confined in the potential cnergy well 0 V(x) = { 0 <r <L elsewhere 2.33. Evaluate (x), (Px), A.x, APx, and Ax Ape for the normalized wave function { (x) = sin 0<x<L 0 elsewhere In the next chapter we will...
If X and Y have a joint probability density function specified by 2-(+2y) find P(X <Y).
7. Show that if the joint probability density function of X and Y is if 0 < x <.. =sin(x + y) f(x, y) = { VI fres 9 Line + »» Hosszž, osys elsewhere, then there exists no linear relation between X and Y.
function Ckek osrs4 be a density 4. Let f(x)=3 otherwise Find: i) k = 24] P(-2<x<2)
FInd u(x,t) and lim u(x,t) Solve the heat problem Ut = Uzx + 5 sin(4x) - sin(2x), 0 < x <7, u(0,1) = 0, u(,t) = 0 u(x,0) = 0
Y(x) A -2 +2 х Extra Credit worth 5 pts: The graph above represents a wave function (x) for a particle confined to -2.00 m < x < 2.00 m. What is the normalized wave function w(x) in the region where -2.00 m <x< 2.00 m? (Show ALL work!) 1 2 Ows + 1 4 o x+2 4 0 w x2+2x+4 16 -(x+2)
Am = } $(w). cos(mkr)dx Bm= f(x) = sin(mkr)dx - Given the periodic quadratic periodic function f(x) = G) "for - <x< . Calculate Ag. There is a figure below that you should be able to see. You may (may not) need: Jup.sin(u)du = (2-u?)cos(u) +2usin(u) /v2.cos(u)du = 2ucos(u)+(u2–2)sin(u) -N2 0
Problem 3. The random variable X has density function f given by 0, elsewhere (a) Assuming that 6 0.8, determine K (b) Find Fx(t), the c.d.f. of X (c) Calculate P(0.4 <X < 0.8)