An authoritative, mathematically rigorous textbook designed specifically for the Quantum Mechanics and Relativity syllabus of the UGTRB Physics Examination. Spanning 14 comprehensive chapters, it provides deep theoretical explanations and derivations for the failure of classical physics, de Broglie matter waves, the Davisson-Germer experiment, wave-particle duality, the photoelectric effect, photomultiplier tubes, the Compton effect, wave nature of electrons, Heisenberg's uncertainty principle, time-dependent and time-independent Schrödinger equations, quantum operators, particle in a box, potential barrier tunnelling, and the special theory of relativity. Includes comprehensive numerical examples and competitive MCQs.