[Wonder Lab #1] Mathematical proof of Schrödinger's equation (Log: July 12, 2026)

Log Date: July 12, 2026 Welcome to the first episode of [Wonder Lab], a new series where I take a deep dive into the mathematical and theoretical foundations of physics. In this session, I'm presenting a formal proof regarding the Schrödinger equation. My goal is to demonstrate that the total probability of finding a quantum particle across all space remains constant over time—meaning dP/dt equals zero. Through a step-by-step whiteboard derivation, I walk through writing the wave equation, applying the complex conjugate, and simplifying the integrand into a perfect derivative. Finally, by analyzing the boundary terms at infinity, I showcase why a real physical particle cannot exist infinitely far away, completing the proof. This session was recorded with a dedicated microphone and improved lab lighting to ensure the complex equations are as clear to watch as they are to solve. DK --- #WireAndWonder #WonderLab #QuantumMechanics #SchrodingerEquation #PhysicsProof #WhiteboardDerivation #ProbabilityConservation #STEM #StudentPhysicist #2026Archive