Problem 1.11 | Griffiths' Introduction to Quantum Mechanics | 3rd Edition

Problem 1.11
[This problem generalizes Example 1.2.] Imagine a particle of mass
m and energy E in a potential well , sliding frictionlessly back and forth
between the classical turning points (a and b in Figure 1.10). Classically, the
probability of finding the particle in the range dx (if, for example, you took a
snapshot at a random time t) is equal to the fraction of the time T it takes to
get from a to b that it spends in the interval dx:
(a) Use conservation of energy to express in terms of E and V(x).
(b) As an example, find for the simple harmonic oscillator, 1/2kx^2. Plot , and check that it is correctly normalized.
(c) For the classical harmonic oscillator in part (b)...

In this video, we solve Problem 1.11 in Griffiths' Introduction to Quantum Mechanics (3rd Edition) as part of a series of solutions to the textbook's questions.