Quantum Mechanics through Problems
With Complete Solutions

More than 300 problems in quantum mechanics, primarily at graduate or upper-undergraduate level, along with detailed and extensive solutions.

Rocco Schiavilla (Author)

9781009473620, Cambridge University Press

Paperback / softback, published 12 December 2024

784 pages
25.4 x 20.2 x 4 cm, 1.59 kg

This book contains more than 300 problems in quantum mechanics with accompanying solutions, covering topics that are commonly taught in first-year graduate physics programs. Special care is given to each problem's formulation, with detailed and extensive solutions provided to support understanding. The problems span a range of difficulties, from basic exercises to more challenging applications and extensions of the standard material. Students are required to think critically and incorporate physics and mathematical techniques learned previously or concurrently to solve the more challenging problems. Each chapter begins by framing the particular topic being examined with a short theory section that sets the context for and motivates the problems that follow. This text is well suited for self-study or as a useful supplement to the existing quantum mechanics textbooks for upper-undergraduate and graduate students, and their instructors.

1. The failure of classical physics
2. Wave-particle duality and wave mechanics
3. Schrödinger equation: uncertainty relations
4. The one-dimensional Schrödinger equation: bound states
5. Scattering in one dimension
6. Mathematical formulation of quantum mechanics
7. Physical interpretation: postulates of quantum mechanics
8. The harmonic oscillator
9. Particle in a central potential: orbital angular momentum
10. Bound states in a central potential: applications
11. Angular momentum: general properties
12. Spin: charged particle in an electromagnetic field
13. Addition of angular momenta
14. Approximation methods
15. Scattering by a potential
16. Symmetry transformations of states and operators
17. Rotation matrices and the Wigner–Eckart theorem: fine and hyperfine structure of energy levels in hydrogen-like atoms
18. Time-dependent perturbation theory
19. Systems of identical particles
Bibliography
Index.

Subject Areas: Quantum physics [quantum mechanics & quantum field theory PHQ]