x Contents 2.5.3 The position and momentum eigenstates;momen- tum as a translation operator 2.6 Completeness 45 5 Problems 47 Numerical analyses 8 3 The Schrodinger equation g 3.1 General properties 3.1.1 Boundary conditions 49 3.1.2 Ehrenfest's theorem 3.13 Current density and conservation of probability 3.1.4 The virial and Feynman-Hellman the 52 3.2 One-dime 54 Topologically nontrivial 5 3.2.3 Special properties of on-dimensional Schrodinger equations 3.3 Potential wells 3.3.1 Infinitely deep wells(walls) 58 3.3.2 The finite square well 3.3.3 An application 可 3.4 The harmonic oscillator 63 3.4.2 Creation and annihilation 3.5 Scatterin and the 3.5.1 the t unnel effect 352 potentia 74 35.3 General aspects of the scattering problem 3.6 Periodic potentials 3.6.1 The band structure of the energy spectrum 80 3.62 Analysis 82 Guide to the Supplements Problems 8 Numerical analyses 4 Angular momentum 89 4.1 Commutation relations 4.2 Space rotations 4.3 Onantization 4.4 The Stern-Gerlach experiment Spherical harm Matrix e 4.6.1 4.7 The composition rule 101 4.7.1 The Clebsch-Gordan coefficients 4.8 Spin 105 4.8.1 Rotation matrices for spin Guide to the Supplements 108