Theproof that the classical value of x 2 is L 2 12 .

Question

Want to see the full answer?

Answer 1

Question

Chapter 35, Problem 31P

(a)

To determine

Theproof that the classical value of x2 is L212 .

(b)

To determine

The proof that the quantum expectation value of x2 for the nth state of the particle is L212 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

A quantum particle in an infinitely deep square well has a wave function given by ψ2(x) = √2/L sin (2πx/L)for 0 ≤ x ≤ L and zero otherwise. (a) Determine the expectation value of x. (b) Determine the probability of finding the particle near 1/2 L by calculating the probability that the particle lies in the range 0.490L ≤ x ≤ 0.510L. (c) What If? Determine the probability of finding the particle near 1/4L bycalculating the probability that the particle lies in the range 0.240L ≤ x ≤ 0.260L. (d) Argue that the result of part (a)does not contradict the results of parts (b) and (c).

*24 Figure 39-30 shows a two-dimen- sional, infinite-potential well lying in an xy plane that contains an electron. We probe for the electron along a line that bisects L, and find three points at which the detection probability is maximum. Figure 39-30 Problem 24. Those points are separated by 2.00 nm. Then we probe along a line that bisects L, and find five points at which the detection probability is maximum. Those points are sep- arated by 3.00 nm. What is the energy of the electron?

If the particle in the box in the second excited state(i.e. n=3), what is the probability P that it is between x=L/2 and x=L/3 ?