Quantum-Confined Stark Effect 2D: Tilted-Well Band Diagram

This is the 2D companion to the 3D strain-induced piezoelectric quantum-dot simulator. Rather than an isometric render of a wavefunction cloud, it solves the actual effective-mass Schrodinger equation for the electron and the hole along the dot's growth axis: each is a particle confined to an infinite square well of width equal to the dot height, tilted by the internal piezoelectric field computed from the same alloy-interpolated strain physics as the 3D sim. The tilted-well Hamiltonian is diagonalized in a 30-state particle-in-a-box basis using an in-browser Jacobi eigenvalue solver, giving genuine, nonperturbative ground-state energies and envelope wavefunctions instead of a fitted separation curve. The resulting band diagram shows the electron and hole probability densities pulled toward opposite faces of the well, and the live readouts — separation, redshift, and wavefunction overlap — are all read directly off the computed eigenstates.