Pro Tier Module
1D Schrodinger Eigensolver
Diagonalize a 1D quantum Hamiltonian and check the spectrum against published exact eigenvalues.
See it run - a worked example, 100% in this browser tab
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.
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.