Fisica Generale 3

Quantum mechanics 

Introduction to interference experiments with both light and massive particles 

Observation of atomic spectra

1) Schrödinger equation

1.1) Introduction and motivation

1.2) Limits of the classical description 

1.3) Wavefunction and wave equation

1.4) Statistical interpretation of the wavefunction

1.5) Solution of the free Schrödinger equation

1.6) Expectation values and operators

Hilbert space formalism I: scalar product and linear operators

1.7) Commutation relations and dynamics of expectation values

1.7.1) Ehrenfest theorem

1.7.2) Uncertainty relations

2) Stationary states and energy spectrum 

2.1) Time independent Schrödinger equation

2.2) Harmonic oscillator

2.2.1) Parity operator
 
2.3) Continuous spectrum

Hilbert space formalism II:

II.I) Vectors

II.II) Linear operators

II.III) Projections

II.IV) Spectral representation of self-adjoint operators

3) Motion in central force field

3.1) Angular momentum operators

3.2) Spherical harmonics

3.3) Bound states in central force field

3.4) Coulomb potential and hydrogen atom

Hilbert space formalism II:

II.V) Projection-valued measure 

II.VI) Statistical operator

II.VII) Unitary operators

QM) General formulation of quantum
mechanics as a probability theory

QM.1) Quantum mechanics as statistical theory

QM.1.I) Hilbert space

QM.1.II) State

QM.1.III) Observable

QM.1.IV) Probability formula

QM.1.V) Time evolution

QM.2) Measurement in quantum mechanics

QM.2.I) Measurement with and without outcome reading 

QM.2.II) Sequential measurements 

QM.2.III) Amplitude vs probabilities

CS.1) Composite systems and tensor product structure

CS.2) Bell inequalities