Deep-Dive Guides · Quantum Chemistry
Quantum Chemistry — the complete deep dive
The postulates, the four exactly solvable models, operators and angular momentum, and the approximation methods that reach real molecules.
Free extract — the opening section of the guide, in full.
0. How to use this guide — the quantum recipe
Every model in this guide is the same four steps. Learn the pattern once; the four "hard" systems differ only in their potential V and boundary conditions.
write Ĥ = T̂ + V̂ → solve Ĥψ = Eψ → apply boundary/normalisation → read En, ψnthe recipe
| Model | Potential V | Quantum number(s) | Energy pattern | Chemistry it models |
|---|---|---|---|---|
| Particle in a box | 0 inside, ∞ walls | n = 1,2,3… | E ∝ n² | π-electrons, quantum dots, translation |
| Harmonic oscillator | ½kx² | v = 0,1,2… | E ∝ (v+½), even spacing | vibrations, IR/Raman |
| Rigid rotor | 0 (fixed r) | J = 0,1,2… | E ∝ J(J+1) | rotations, microwave spectra |
| Hydrogen atom | −Ze²/4πε₀r | n, l, ml | E ∝ −1/n² | atomic orbitals, all of chemistry |
The three questions to ask of any quantum problem: (1) What is the potential and what are the boundary conditions? (these quantise the energy — confinement ⇒ discrete levels). (2) Is the operator I need Hermitian, and does it commute with Ĥ? (commuting ⇒ simultaneous eigenstates / a good quantum number). (3) Is the system exactly solvable, or do I need an approximation (variation / perturbation)? Answer these three and you know which tool to reach for.
Read the rest of this guide
The remaining 10 sections — Postulates, operators & uncertainty, Particle in a box, Harmonic oscillator, Rigid rotor & angular momentum and more — are part of ChemVidya Full Access, along with the other guides, the books, the study notes and 6,000+ practice questions with worked solutions.