Introductory quantum chemistry 0600-S1-O-PCK

Lecture:

1. Why quantum mechanics:
a) Quantum theory – black-body radiation
b) Photoelectric effect
c) Compton effect
d) Planetary model of the atom: Bohr's postulates, successes and failures
e) de Broglie hypothesis
f) Wave nature of electrons
g) Heisenberg uncertainty principle and wave packet
h) Defining the state of a system in classical vs. quantum mechanics
2) Postulates of quantum mechanics (according to Kołos)
3) Simple applications of quantum mechanics:
a) Free particle
b) Particle in a 1D potential well (box)
c) 1D harmonic oscillator
d) Morse oscillator and Lennard-Jones potential
e) Particle on a ring
f) Rigid rotor
g) Vibrational-rotational spectrum
4) Hydrogen atom and hydrogen-like ions:
a) Quantum numbers
b) Orbitals
c) Radial probability density
d) Determination of hydrogen atom spectral lines
5) Approximate methods in quantum mechanics:
a) Variational method
b) Ritz method
6) Symmetry of the many-electron wavefunction:
a) Spin, spin function, total spin
b) Indistinguishability of identical particles
7) One-electron approximation:
a) Sum of one-electron Hamiltonians
b) Ground-state wavefunction for the He atom
c) Spin-orbital
d) N-electron wavefunction (Slater determinant)
e) Hartree product
8) LCAO MO approximation and the concept of a basis set

Exercises – problems concerning the following topics:

1) Basic physical quantities of mechanics (r, v, p, M, T, V, E) - only if 1st exercise precedes 1st lecture!
2) Tasks regarding postulates (see Kołos): class Q of the wave function, normalization of the wave function, volume element in Cartesian and spherical coordinates, form of operators (especially Hamiltonians, e.g. for the hydrogen atom, helium atom, general for the M-nuclear and N-electron systems) and checking their Hermitian character, commutators, average value of the operator, etc.
3) Particle in the box - probability in
4) Harmonic oscillator
5) Rigid rotator
6) Hydrogen atom
7) Variation method and Ritz method
8) LCAO approximation

Computer lab – Maxima basics:

1) Basic operations
2) Functions
3) Function plots
4) Special functions:
a) Hermite polynomials
b) Legendre polynomials
c) Associated Legendre polynomials
d) Spherical harmonics
e) Laguerre polynomials
5) Using WxMaxima to solve problems from the exercises