Measurements of the position x (in units of cm) of a particle are governed by the probability density P(x) = A(1 - x^2) negative 1less than or equal to x less than or equal to 1 (a) Determine A. (b) Find the expectation values and . (c) What is the probability that a measurement of the particle's position yields a result between 0 and 0.5? (d) If your classmates and you each performed one measurement of the position of the particle, what do you expect the spread in your measurement results to be?

Question

Measurements of the position x (in units of cm) of a particle are governed by the probability density P(x) = A(1 - x^2) negative 1less than or equal to x less than or equal to 1 (a) Determine A. (b) Find the expectation values < x > and < x2 >. (c) What is the probability that a measurement of the particle's position yields a result between 0 and 0.5? (d) If your classmates and you each performed one measurement of the position of the particle, what do you expect the spread in your measurement results to be?