Space Quantization 2D: Angular Momentum Vector Diagram

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 2D simulator draws the resulting "space quantization" as the classic textbook vector-model diagram — a cone in oblique projection, a live Lx–Ly precession-circle plot, and a quantized Lz-level ladder — so you can see the same physics from three complementary 2D views at once. Live readouts track |L|, Lz, the cone half-angle θ and the current azimuth, and a toggle reveals every allowed m_l cone for the chosen l at once.