Fundamentals of quantum chemistry 0600-S1-EN-FQCh

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 and the wave nature of electrons
f) Heisenberg uncertainty principle and wave packet
g) defining the state of a system in classical vs. quantum mechanics
2) Postulates of quantum mechanics
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 and vibration-rotation 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
e) Hartree product
8) LCAO MO approximation and the concept of a basis set

Exercises – problems concerning the following topics:

1) Fundamental mechanical quantities (r, v, p, M, T, V, E) -- only if the first tutorial precedes the first lecture!
2) Problems concerning postulates (see Kołos), e.g., the Q class of the wave function, wave function normalization, volume elements in Cartesian and spherical coordinates, the form of operators (especially Hamiltonians—e.g., for the hydrogen atom, helium atom, or the general case of an M-nucleus/N-electron system) and verifying their Hermiticity, commutators, expectation values ​​of operators, etc.
3) Particle in a box – probability within the interval
4) Harmonic oscillator
5) Rigid rotor
6) Hydrogen atom
7) Variational method and Ritz method
8) LCAO approximation

Computer laboratory – learning the basics of the WxMaxima package:

1) Mathematical functions
2) Examples of use in solving and illustrating specific problems from the tutorials