Potential Energy in the quantum SHO

Here I review the SHO from Griffiths, with a touch of Dirac notation. This problem is incredibly useful in highlighting SHO problems and their approach using the creation annihilation operators. I also mean for this to provide a bit of a stepping stone into Dirac notation, while leaving the wave function approach to Griffiths for readers to review to in order to see how this notation actually works.

What textbooks are recommended?

For students of both undergraduate and graduate level, if there is a Griffiths textbook for the topic you are currently investigating, that is what I would recommend. For undergraduates, Griffiths provides a wonderful introduction to each subject. His books contain adequate theory and mathematical principles, numerous examples, and an insane number of useful problems to work through to ensure a students grasp of the material(as well as a good dashing of humor). I actually have a habit of placing a blue sticky note in a book when I find an illuminating example or problem that can be essential to understanding a concept, and I often find Griffiths texts to be a sea of these blue notes by the time I am finished. I also recommend Griffiths for graduate students, because from my experience if you can understand a majority of the Griffiths text for that subject, it really is trivial to apply graduate concepts to the material(as simple as adding cheese to a burger), and qualifying exams and problems that will be encountered in your research can often be tackled with the depth of the topic that is covered in Griffiths.
Of course aside from physics, there are plenty of textbooks (particularly mathematics) that I find particularly illuminating, and I will bring these up when they are necessary or helpful for the subject that is being tackled.