The Schrödinger equation is a fundamental equation in quantum mechanics that describes the time evolution of the wave function of a quantum system

🧠Derivation of the Time-Dependent Schrödinger Equation

Click Next Step to reveal each stage of the derivation.

Step 1 of

Quantum Wave Function Visualizer

The wave function visualizer represents the particle in a one-dimensional infinite potential well. It shows the variation of wave function ψ(x) and probability density |ψ(x)|² for different quantum numbers. As quantum number increases, the number of nodes increases and energy becomes quantized. The particle can only exist at positions where probability density is non-zero.

Change quantum number and box size to see wave function behavior.

Quantum Number (n): 1

Box Length (L): 1

Blue → Wave Function ψ(x) | Red → Probability Density |ψ(x)|²

📌 Exam Shortcut Box

• Derivation base: de Broglie hypothesis + classical energy equation
• Energy operator: iħ ∂/∂t
• Momentum operator: -iħ ∂/∂x
• Key idea: Replace physical quantities with operators

Quick memory trick: “Energy → time derivative, Momentum → space derivative”