PT-Symmetric Quantum Mechanics: Exceptional Points

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 plots both eigenvalue branches in 3D as the gain/loss strength γ is swept past the coupling κ — watching the spectrum bend from real into complex as probability conservation itself breaks down.