Recommended quantum mechanics books for high school graduates include Griffith's "Quantum Mechanics," noted for its accessible style, though some find it potentially confusing for beginners. A solid understanding of mathematics is essential, particularly in solving partial differential equations, as this is crucial for tackling the Schrödinger equation. Familiarity with special functions and linear algebra is also important, especially when learning about ket notation. Many university-level textbooks may not be suitable for those just finishing high school, as real quantum theory typically begins in the second year of undergraduate studies after foundational courses in analytical mechanics and classical electromagnetism.