Quantum Atomic Structure — Wave Functions, Orbitals & Spin Explained | Chapter 41 of University Physics
Quantum Atomic Structure — Wave Functions, Orbitals & Spin Explained | Chapter 41 of University Physics Chapter 41 extends quantum mechanics into three dimensions, applying Schrödinger’s equation to atomic systems. Explore how quantum numbers define wave functions and orbitals, and uncover the roles of spin, magnetic fields, and entanglement in shaping atomic behavior. Be sure to watch the full video summary for animations of atomic orbitals and spectral line splitting. 3D Schrödinger Equation & Atomic Wave Functions In three dimensions, the time-independent Schrödinger equation −(ħ²/2m)∇²ψ + U(r)ψ = Eψ governs atomic wave functions ψ(x,y,z). These stationary states, when normalized, satisfy ∫|ψ|² dV = 1, giving the probability density for locating electrons in space. Particle in a Cubical Box A particle confined to a cube of side L has energy levels: E = (ħ²π²/2mL²)(n x ² + n y ² + n z ²) , with quantum numbers (n x ,n y ,n z ) = 1,2,3… Degenerate states s...