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Cover -- Half-Title Page -- Title Page -- Copyright Page -- Contents -- Foreword -- Preface -- 1. Schrödinger's Equation and its Applications -- 1.1. Physical state and physical quantity -- 1.1.1. Dynamic state of a particle -- 1.1.2. Physical quantities associated with a particle -- 1.2. Square-summable wave function -- 1.2.1. Definition, superposition principle -- 1.2.2. Properties -- 1.3. Operator -- 1.3.1. Definition of an operator, examples -- 1.3.2. Hermitian operator -- 1.3.3. Linear observable operator -- 1.3.4. Correspondence principle, Hamiltonian

1.4. Evolution of physical systems -- 1.4.1. Time-dependent Schrödinger equation -- 1.4.2. Stationary Schrödinger equation -- 1.4.3. Evolution operator -- 1.5. Properties of Schrödinger's equation -- 1.5.1. Determinism in the evolution of physical systems -- 1.5.2. Superposition principle -- 1.5.3. Probability current density -- 1.6. Applications of Schrödinger's equation -- 1.6.1. Infinitely deep potential well -- 1.6.2. Potential step -- 1.6.3. Potential barrier, tunnel effect -- 1.6.4. Quantum dot -- 1.6.5. Ground state energy of hydrogen-like systems -- 1.7. Exercises

1.7.1. Exercise 1 -- Probability current density -- 1.7.2. Exercise 2 -- Heisenberg's spatial uncertainty relations -- 1.7.3. Exercise 3 -- Finite-depth potential step -- 1.7.4. Exercise 4 -- Multistep potential -- 1.7.5. Exercise 5 -- Particle confined in a rectangular potential -- 1.7.6. Exercise 6 -- Square potential well: unbound states -- 1.7.7. Exercise 7 -- Square potential well: bound states -- 1.7.8. Exercise 8 -- Infinitely deep rectangular potential well -- 1.7.9. Exercise 9 -- Metal assimilated to a potential well, cold emission

1.7.10. Exercise 10 -- Ground state energy of the harmonic oscillator -- 1.7.11. Exercise 11 -- Quantized energy of the harmonic oscillator -- 1.7.12. Exercise 12 -- HCl molecule assimilated to a linear oscillator -- 1.7.13. Exercise 13 -- Quantized energy of hydrogen-like systems -- 1.7.14. Exercise 14 -- Line integral of the probability current density vector, Bohr's magneton -- 1.7.15. Exercise 15 -- Schrödinger's equation in the presence of a magnetic field, Zeeman-Lorentz triplet -- 1.7.16. Exercise 16 -- Deduction of the stationary Schrödinger equation from the De Broglie relation

1.8. Solutions -- 1.8.1. Solution 1 -- Probability current density -- 1.8.2. Solution 2 -- Heisenberg's spatial uncertainty relations -- 1.8.3. Solution 3 -- Finite-depth potential step -- 1.8.4. Solution 4 -- Multistep potential -- 1.8.5. Solution 5 -- Particle confined in a rectangular potential -- 1.8.6. Solution 6 -- Square potential well: unbound states -- 1.8.7. Solution 7 -- Square potential well: bound states -- 1.8.8. Solution 8 -- Infinitely deep rectangular potential well -- 1.8.9. Solution 9 -- Metal assimilated to a potential well, cold emission

1.8.10. Solution 10 -- Ground state energy of the harmonic oscillator

Includes bibliographical references and index.

Quantum mechanics is the foundation of modern technology, due to its innumerable applications in physics, chemistry and even biology. This second volume studies SchrOdinger's equation and its applications in the study of wells, steps and potential barriers. It examines the properties of orthonormal bases in the space of square-summable wave functions and Dirac notations in the space of states. This book has a special focus on the notions of the linear operators, the Hermitian operators, observables, Hermitian conjugation, commutators and the representation of kets, bras and operators in the space of states. The eigenvalue equation, the characteristic equation and the evolution equation of the mean value of an observable are introduced. The book goes on to investigate the study of conservative systems through the time evolution operator and Ehrenfest's theorem. Finally, this second volume is completed by the introduction of the notions of quantum wire, quantum wells of semiconductor materials and quantum dots in the appendices.