Morse V(r_e) = 0, V(r_e + ln 2/a) = D_e/4 (quarter-well anchor exact)

Sympy-exact witness of two canonical Morse anchors. At r = r_e: V = D_e (1 − e^0)² = D_e · 0 = 0 (equilibrium minimum). At r = r_e + ln 2 / a: exp(−a · ln 2/a) = exp(−ln 2) = 1/2, so V = D_e(1 − 1/2)² = D_e/4 (quarter-well). Oracle…