Contents Preface page xvii Physical constants 1 Basic formalism 1.1 State vectors 1.2 Operators and physical observables 13 Eigenstates 14 Hermitian conjugation and Hermitian operators Hermitian operators:their eigenstates and eigenvalues 6 1.6 Superposition principle 1.7 Completeness relation 18 Unitary operators 1.9 Unitary operators as transformation operators 10 1.10 Matrix formalism 1.11 Eigenstates and dia agonalization of matrices 1.12 Density operator 1618 1.13 Measurement 20 1.14 Problems 21 2 Fundamental commutator and time evolution of state vectors and operators 24 2.1 Conti s variables:and P operators Canonical commutator [X,P] 246 2.3 P as a derivative operator:another way 29 2.4 X and P as Hermitian operators 5 Uncertainty principle 32 2.6 Some interesting applications of uncertainty relations 27 Space displacement operator 36 28 Time evolution operat Appendix to Chapter 2 4 2.10 Problems 3 Dynamical equations 55 3.1 Schrodinger picture 3.2 Heisenberg picture 57 Contents Preface page xvii Physical constants xx 1 Basic formalism 1 1.1 State vectors 1 1.2 Operators and physical observables 3 1.3 Eigenstates 4 1.4 Hermitian conjugation and Hermitian operators 5 1.5 Hermitian operators: their eigenstates and eigenvalues 6 1.6 Superposition principle 7 1.7 Completeness relation 8 1.8 Unitary operators 9 1.9 Unitary operators as transformation operators 10 1.10 Matrix formalism 12 1.11 Eigenstates and diagonalization of matrices 16 1.12 Density operator 18 1.13 Measurement 20 1.14 Problems 21 2 Fundamental commutator and time evolution of state vectors and operators 24 2.1 Continuous variables: X and P operators 24 2.2 Canonical commutator [X , P] 26 2.3 P as a derivative operator: another way 29 2.4 X and P as Hermitian operators 30 2.5 Uncertainty principle 32 2.6 Some interesting applications of uncertainty relations 35 2.7 Space displacement operator 36 2.8 Time evolution operator 41 2.9 Appendix to Chapter 2 44 2.10 Problems 52 3 Dynamical equations 55 3.1 Schrödinger picture 55 3.2 Heisenberg picture 57