Chapter 8 - Hints for exercises and problems:

Omit the parts of the problems that include sin³q

1 W = 1 J s

(1 Watt = 1 Joule second)

Exercise 8.6 - speed is impacted by the number of photons (since momentum is)

Exercise 8.7 - power is rage of energy emission

Above is how we can get energy per photon

Problem 8.5 - radius of sphere =

Problem 8.8 - include a factor of 2 in the wavefunction

Problem 8.13 - Useful trig relationship:

Problem 8.14b - Look at the last part - related to phi - solve this part first!

Other suggestions/hints:

Do not let unusual integrals bother you to the extent that they detract from the main point of the problem. What are you doing, and why are you doing it? (e.g, are you looking for an average value of a property, a normalization constant?) (I am convinced that the author put some of the problems involving unusual integrals are to aid you in learning how to not panic when you see anything out of the ordinary!)

Simply find the appropriate integration formula (for the non-basic integrals), and plug in the needed interpretation. Some of them are given below:

For your encounter of the following integral, it will be equal to zero. (Note that this is not always the case.)

For your encounter of the following integral, it is equal to zero, by symmetry, as x is an odd function.