Quantum Chemistry Lecture Notes Pdf Verified Jun 2026

Quantum Chemistry — Concise Lecture Notes (PDF-ready) 1. Introduction

Scope: Quantum mechanics applied to atoms, molecules, electronic structure, spectroscopy, and chemical bonding. Prerequisites: Undergraduate quantum mechanics, linear algebra, calculus, basic physical chemistry.

2. Fundamental Postulates

State of system = wavefunction ψ(r, t); |ψ|^2 gives probability density. Observables → Hermitian operators Â; measurement yields eigenvalues. Time evolution: Schrödinger equation, time-dependent and time-independent forms. quantum chemistry lecture notes pdf verified

Time-dependent: iħ ∂ψ/∂t = Ĥψ Time-independent (stationary): Ĥψ = Eψ

3. Operators, Expectation Values & Commutators

Expectation: ⟨A⟩ = ∫ψ*  ψ dτ. Hermitian:  = †. Commutator: [Â, B̂] = ÂB̂ − B̂Â; if zero, simultaneous eigenstates exist. Uncertainty principle: ΔA ΔB ≥ (1/2)|⟨[Â,B̂]⟩|. Quantum Chemistry — Concise Lecture Notes (PDF-ready) 1

4. One-electron Systems

Particle in a box, harmonic oscillator — quantized energies, eigenfunctions. Hydrogen atom:

Hamiltonian in spherical coords, separation into radial and angular parts. Quantum numbers n, l, m; energy En = −(μe^4)/(2ħ^2 n^2). Spherical harmonics Y_l^m(θ, φ). Quantum numbers n

5. Approximation Methods

Variational principle: E0 ≤ ⟨ψ_trial|Ĥ|ψ_trial⟩/⟨ψ_trial|ψ_trial⟩. Time-independent perturbation theory: