Pro Tier Module
1D Schrodinger Eigensolver
Diagonalize a 1D quantum Hamiltonian and check the spectrum against published exact eigenvalues.
This tool runs inside GDBS Pro. What it computes and the authorities it applies are below.
The problem
Quick quantum eigenvalue checks usually mean a notebook and a library, with no built-in validation against the textbook exact spectrum.
The local-first solution
This plugin builds H = -1/2 d2/dx2 + V(x) by finite differences and diagonalizes the tridiagonal matrix with a Jacobi sweep in the browser, reporting the true error of the computed spectrum against the published exact eigenvalues.
What it does
Finite-difference Hamiltonian on a uniform grid for harmonic, box, and finite-well potentials
Cyclic Jacobi rotation diagonalization of the symmetric tridiagonal matrix
Eigenvalues validated against published harmonic E_n = n + 1/2 and box E_n = n^2 pi^2 / 2L^2
True relative eigenvalue error mapped to the trust verdict
Precision-decade readout from the measured residual
Honest scope
This is a finite-difference, finite-grid approximation; the reported error is the genuine discretization plus boundary-truncation error versus the cited exact spectra. EXACT is never claimed - a finite-difference spectrum is never bit-exact against the continuum. The finite square well has no elementary closed form, so its trust is honestly untracked.
Authorities cited
- Griffiths, D. J. (2005). Introduction to Quantum Mechanics, 2nd ed. - harmonic oscillator (Ch. 2.3, E_n = (n + 1/2) hbar omega) and infinite square well (Ch. 2.2, E_n = n^2 pi^2 hbar^2 / 2 m L^2).
- Standard three-point finite-difference discretization of the 1D stationary Schrodinger eigenproblem on a uniform grid.
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Solve a 1D eigenproblem
Diagonalize the Hamiltonian in the browser and save the validated spectrum to Sandbox, attach it to a Worklog case, or route it into a Gate client portal. Nothing is uploaded to anyone's cloud.