Question

3. At time t-0 a particle is represented by the wave function A-if 0 < x<a ψ(x,0) = 0 otherwise where A, a, and b are constants. a) Normalize ψ(x,0). b) Draw (x,0). c) Where is the particle most likely to be found at t-0? d) What is the probability of finding the particle to the left of a? e) What is the expectation value of x?

Answer 1

Normaliz the function. 1=Ly'ydx dr - x -x Jab- ab-a - II A 1= (A *19 v*d+(64116=xtºck 1- (A) prd={A} [(6+2 -26)dt T0-03) (02.Byl tor) 21, b + a' 2 ba

16) (x,0) X Consider A, a, and b are positive constants. The above diagram is the plot of function v (0,x). Since the slope of the function for 0 < x Sa is positive and slope for a sxsb is negative hence, the plot will look like as the above plot. (c) From the graph of the partical's wavefunction it is clear that the maximum valu of y(x,0) is maximum at a. (d) Probability of finding the particle to the left of a is, 5*4* (x:)dx= 10 (44)