PT-Symmetric Quantum Mechanics: Eigenvalue Map

Ordinary quantum mechanics requires a Hermitian Hamiltonian so that energies stay real and probability is conserved. PT-symmetric quantum mechanics studies a broader class of non-Hermitian Hamiltonians — balanced gain paired with balanced loss — that can still produce a fully real energy spectrum, right up until a critical "exceptional point" where the two eigenvalues and their eigenvectors collide. This simulator builds the simplest such system, a two-level gain/loss pair, integrates its Schrödinger equation live, and lays out three linked panels — an eigenvalue map, a scrolling population chart, and an orbiting population view — so you can watch the spectrum bend from real into complex as probability conservation itself breaks down.