ABSTRACT
Since the main purpose of the book was to demonstrate the philosophy and spirit behind the standard formulation of quantum mechanics, a thorough discussion of applications have taken a somewhat backseat. This was also done to keep the book accessible to a wide audience. Even outsiders interested to get a glimpse of quantum mechanics could get by with some minimal linear algebra provided in the book itself. Thus, technical and calculational details (which cannot be avoided if one were to discuss applications) had to be mostly avoided in the main text. However, in order that the book could still serve as an introductory text for a mainstream course, we make an exception in this chapter. Here we treat three of the mostwell known applications of quantum mechanics: Harmonic Oscillator, Angular Momentum and Hydrogen Atom. Both the analytical and the algebraic, ladder operator methods are demonstrated for solving the eigenvalue problems for the Harmonic oscillator and angular momentum. Topics involving technical calculations (e.g., calculations involving Hermite polynomials, spherical harmonics, etc.), modelling of real life systems (e.g., atomic polarizability) and spin have been relegated to the problem sets with elaborate hints and guidelines for working through them.
