At least a few books have "Quantum Mechanics" in their title, e.g., Sakurai's Modern Quantum Mechanics. However, I don't think measuring spin, which is "the" way of introducing quantum mechanics, concerns itself with mechanics, the study of motion. It seems to me that these books ought to have "Quantum Physics" in their titles as opposed to "Quantum Mechanics". "Quantum Physics" better encapsulates what these books cover. What's the deal with this?
closed as primarily opinion-based by ZeroTheHero, Alfred Centauri, John Rennie, Aaron Stevens, user191954 Oct 6 '18 at 4:36
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There is no "deal with this," really. Mechanics has to do with motion, and a very early motivation for why/how quantum physics was discovered was asking precisely the question, "how do atoms move?" No better a theory than quantum mechanics tells you how atoms, or electrons, or any subatomic particle moves, hence "mechanics." That said, the phrases "quantum mechanics," "quantum physics," and "quantum theory" are practically used interchangeably.
Spin is a usual starting point in introductory QM books generally since it is 1) conceptually simple, 2) pedagogically instructive since what a student learns from the spin example is applicable elsewhere. It's also a great starting point for getting comfortable with Dirac notation (i.e. David McIntyre's book).
Furthermore, standard quantum mechanics, and quantum dynamics, is fundamentally similar to classical mechanics in terms of algebraic properties (of course the Hilbert space of quantum mechanics is very unclassical). As Sakuri remarks on page 48, Dirac's correspondence principle is that you take the classical mechanical Poisson bracket, replace it with a commutator and divide by $i\hbar$ and now you have the quantum mechanical structure. This is true since the Poisson bracket and the commutator produce similar algebras. This fact is illuminated in the Heisenberg Picture, where the Heisenberg equation of motion is used (which is reminiscent of the classical mechanical analogue), trajectories are found, and commutators are everywhere!
So there are many reasons why you'd want to call the quantum theory of motion "Quantum Mechanics."
EDIT: The OP might find the following link useful: Are quantum mechanics and quantum physics the same field?
Classical Mechanics (CM) and Quantum Mechanics (QM) are both mechanics in the sense that they give rules for calculating the evolution of the dynamical variables (position, momentum, angular momentum etc) a system in time through the Newton's/Hamilton's equation of motion (for CM) or Schrodinger equation (for QM). Moreover, Quantum Physics concerns everything i.e., non-relativistic quantum mechanics to relativistic quantum field theory.