Chapter 6 showed that a taller rectangular barrier (larger
PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Symmetry, angular momentum and spin · Symmetry, angular momentum and spin
Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Spin one-half, the Pauli matrices and two-level systems
Problem
Chapter 6 showed that a taller rectangular barrier (larger V0−E, hence larger κ=2m(V0−E)/ℏ) suppresses tunnelling transmission exponentially, T≈16E(V0−E)V0−2e−2κa. The nitrogen crossing ammonia's barrier is exactly this kind of tunnelling, though Δ is fixed by the measured line rather than computed from the barrier. Suppose a related molecule had a taller barrier between its two configurations than ammonia's, with everything else the same. Without computing a new value for Δ, say whether this molecule's inversion line would sit above or below ammonia's 23.9GHz, and whether its crossing time would be longer or shorter than ammonia's 2.1×10−11s, giving the chain of reasoning that connects the two chapters.