Schrödinger Equation
The Schrödinger equation governs how a quantum state evolves over time: iħ∂t|ψ⟩ = Ĥ|ψ⟩, where Ĥ is the Hamiltonian (the energy operator). Key properties include linearity (ensures superposition holds through time), unitarity (probability is conserved), and determinism (the evolution is continuous and reversible until measurement). This equation is not only the foundation of quantum mechanics, it's the differential heartbeat of all quantum computation.
Quantum Energy Simulation (Particle in a Box)
Visualizing the Time-Independent Schrödinger Equation for the simplest bound system.
Quantum Control
n=1 (Ground)n=4 (Excited)
Key Concepts
Quantized Energy (Eₙ)
Energy is proportional to n².
Probability Density (|Ψₙ|²)
Shows the likelihood of finding the particle at a given position.
Energy Levels & Probability Density (|Ψ|²)
Selected State
n=1
Energy (Relative)
9.87
Wavelength
2.00