The limitations of Classic Physics and the origins of Quantum Mechanics; revision of basic concepts of Modern Classic Mechanics; preliminary presentation of some key concepts regarding Quantum Mechanics.
2. The Wave Function:
Presentation of Schrödinger equation; the wave function and its interpretation; normalization and conservation of the norm; wave packets; expectable value of an observable, the observable – position and amount of movement and their commutation relations; preliminary presentation of the uncertainty relation position-linear momentum.
The Schrödinger equation in unidimentional problems.
Generic resolution of Schrödinger equation; stationary and non-stationary states and their properties; the principle of the superposition of states. Resolution of time-independent Schrödinger equation in different cases: the Square Well Potential, tunnelling problems, free particle, the harmonic oscillator.
The mathematical formalism of Quantum Mechanics.
The operators in Quantum Mechanics; properties of the hermitian operators; function spaces; Hilbert spaces; the physical Hilbert space. Product of the uncertainties of non-commuting observables; re-analysis of the uncertainty relations; the special case of time-energy uncertainty relation – its interpretation. Introduction to Dirac notation. Angular momentum.
Orbital angular momentum; intrinsic values and intrinsic vectors of L2 and L z; quantification of the angular momentum; introduction to the concept of Spin; the operators J2, J z, J + and J- – properties and usefulness; spin formalism; addition of angular momentum.
Particles in three dimensional potentials.
Gases of free particles. Schrödinger equation in spherical coordinates; radial equation and angular equation; discussion of the solutions for the spherical potential well and for the hydrogen atom; quantification of the energy.
Time independent perturbation theory for non-degenerated states; first-and second order corrections of energy and first-order corrections of the wave function. Time independent perturbation theory for degenerated states. Time-dependent perturbation theory: first order transition probability, state continuum transition; Fermi’s Golden Rule.
Bibliography of reference
CAPRI, A. Z. (1985). Nonrelativistic Quantum Mechanics. Benjamin/Cummings Publishing Company.
COHEN-TANNOUDGI, C.; DIU, B. & LALOË, F. (1973). Mécanique Quantique. Paris: Herman.
GRIFFITHS, D. (1994). Introduction to Quantum Mechanics. London: Prentice Hall Inc.
SINGH, J. (1996). Quantum Mechanics. New York: Jonh Willey & Sons.