ajthor/

schrodinger-dedalus

Numerical solutions to the 1D time-dependent Schrödinger equation with harmonic oscillator potential.

Time-dependent Schrödinger equation: iℏ ∂ψ/∂t = Ĥψ

where the Hamiltonian is: Ĥ = -ℏ²/2m ∇² + V(x)

Harmonic oscillator potential: V(x) = ½mω²x²

The complex wavefunction ψ = ψᵣ + iψᵢ is split into real and imaginary parts:

Real part: ∂ψᵣ/∂t = (ℏ/2m)∇²ψᵢ - V(x)ψᵢ/ℏ
Imaginary part: ∂ψᵢ/∂t = -(ℏ/2m)∇²ψᵣ + V(x)ψᵣ/ℏ… See the full description on the dataset page: https://huggingface.co/datasets/ajthor/schrodinger-dedalus.