Quantum Chemistry / Quantum Mechanics

Prezentace na téma: "Quantum Chemistry / Quantum Mechanics"— Transkript prezentace:

1 Quantum Chemistry / Quantum Mechanics
Computations

2 Recipe 1) Make classical Hamiltonian

3 Recipe 1) Make classical Hamiltonian 2) Replace variables by operators
(In post cases just , i.e.

4 Recipe 1) Make classical Hamiltonian 2) Replace variables by operators
(In post cases just , i.e. 3) Solve SE

5 Recipe 1) Make classical Hamiltonian 2) Replace variables by operators
(In post cases just , i.e. 3) Solve SE 4) Normalize wavefunction

6 Recipe 1) Make classical Hamiltonian 2) Replace variables by operators
(In post cases just , i.e. 3) Solve SE 4) Normalize wavefunction 5) Calculate a property as

7 Example – particle in a box, detailed solution

8 Free particle

9

10 Non-equidistant energy levels
zero “semi-free” movement, still sees the wall

11

12 Harmonic Oscillator

13

14 … zero point energy

15 Harmonic oscillator – general solution
even-separation of energy levels

16 HO wavefunctions excited states- go o classical solution
… ground state, contra-intuitive

17 Radial potential - more dimensions: atoms

18 Radial potential - r +

19 Solution Spherical harmonic functions

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