Determine the normalization constant, C.?

Consider the following probability distribution corresponding to a particle located between pint x=0 and x=a:

P(x)dx= Csin^2 [pi*x/a]dx

a. determine the normalization constant, C.

b. determine <x>.

c. determine <x^2>.

d. determine the variance.

2 Answers

  • a. according to this integral table:

    the integral from 0 to a will be C [(pi/2) - (1/4)sin[2pi]]. Or just C*pi/2.

    so C*(pi/2) = 1 (this is the normalization step)

    so C = 2/pi

    b, c, d: i dont know what you mean by the <>. and i forget how to find variance/ too much work sorry!

  • If ok ( particularly of lambda) is 0 y´´=0 so y´=m and y=mx+n so m could be 0 and y=n (any consistent) If ok is helpful call it w^2 the answer is y=Acos(wx-phi) y´=-Aw sin(wx-phi) y´(0) =0 so sin (-phi)=0 and phi =0 y´(pi))=-Aw sin(w*pi)=0 so wpi=n*pi so w= n( an integer)

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