Space Quantization: Orbital Angular Momentum Vector Model

Quantum orbital angular momentum cannot point in an arbitrary direction: its magnitude |L| = ħ√(l(l+1)) and its projection on the z-axis Lz = m_lħ are fixed by the quantum numbers l and m_l, while the x and y components remain fundamentally undetermined. This simulator renders the resulting "space quantization" as a set of precession cones in 3D — pick l to fix the allowed family of cones, pick m_l to select one, and watch the vector sweep an undetermined azimuth on that cone exactly as the uncertainty relation between L_x, L_y and L_z demands. Live readouts track |L|, L_z, the cone half-angle θ and the current azimuth, and a toggle reveals every allowed m_l cone for the chosen l at once.