This is the 2D companion to the 3D Morse-potential simulator, computed independently from an RK4 integrator rather than a flattened render of the 3D atoms-on-a-spring scene. Instead of watching two 3D spheres oscillate, it draws the same anharmonic bond physics as three genuinely 2D-native graphs stacked together:
V(r) = D_e·[1 − e^(−a(r−r_e))]² − D_e
d²ξ/dτ² = −(1 − e^(−ξ))e^(−ξ), ξ = a(r−r_e), τ = ω₀t
E_n = ħω₀(n+½) − [ħω₀]²/(4D_e)·(n+½)²
- Potential well (top) — V(r) plotted against the real bond stretch, with the quantized levels for the selected molecule shown as bars spanning each level's classical turning points, and the current energy highlighted.
- Phase-space portrait (middle) — a genuinely 2D-only view with no 3D equivalent: it plots the bond's stretch ξ against its momentum-like rate ξ̇ as the RK4 solver advances it. A bound level traces a closed, egg-shaped loop (asymmetric because the well itself is asymmetric); the loop's size grows with n and its shape flattens as the level approaches dissociation.
- Bond animation (bottom) — a simple real-space strip showing the two atoms and the bond stretching and compressing in sync with the graphs above.
- Absorb / Emit photon — jumps to the classical turning point of level n±1 and releases the bond from rest there, exactly like a molecule that just absorbed or emitted an infrared photon of energy ΔE.
- The invariant of motion actually conserved by the integrator is En/De = ξ̇² + (1 − e−ξ)² — verified numerically to drift by less than 10⁻¹³ over two million RK4 steps before this simulator shipped.
- Push n high enough and the phase-space loop no longer closes — the trajectory runs away past ξ ≈ 5.5 and the bond dissociates, exactly as in the 3D sim, and the adjacent-level photon energy ΔE visibly shrinks as levels bunch up near the dissociation limit (real anharmonicity, not a rendering artifact).
All constants (real approximate spectroscopic D_e, r_e, a and reduced mass μ per molecule) are the real physical values; only the animation clock is sped up, since real vibration periods are ~10 femtoseconds.