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Finite Square Well Complete Bound State Energy & Normalized Wavefunctions
x402
Finite Square Well Complete Bound State Energy & Normalized Wavefunctions is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).
Computes all discrete bound-state energy eigenvalues and normalized spatial wavefunctions for a finite symmetric quantum well with specified depth, half-width, effective mass, and query positions.
Price / call$0.003
Success—
StatusUnknown
How this service works
Recover the complete discrete spectrum and normalized spatial states of an explicit finite quantum well.
Output
Returns the complete set of discrete bound-state energy eigenvalues (in eV) and their corresponding normalized spatial wavefunctions evaluated at the requested query positions, covering all even and odd symmetry states supported by the well parameters.
Example use cases
Semiconductor quantum well energy levels
“I'm designing a GaAs/AlGaAs quantum well laser — the well is 4 nm half-width, 0.2 eV deep, effective mass ratio 0.067. Can you give me all the discrete bound-state energies and the normalized wavefunctions sampled at -5, -2, 0, 2, and 5 nm?”
Nanoscale confinement physics homework
“I need to solve a finite square well problem: half-width 2 nm, potential depth 1.5 eV, mass ratio 1.0 (free electron). Please find every bound state energy and evaluate the normalized wavefunctions at positions -3, -1, 0, 1, and 3 nanometers.”
Quantum well wavefunction overlap integral
“For a quantum well with half-width 7 nm, depth 0.5 eV, and effective mass ratio 0.15, give me the full discrete energy spectrum and normalized wavefunction values at -8, -4, 0, 4, and 8 nm so I can compute optical transition matrix elements.”
Technical details
Endpoint
POSThttps://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B009/finite-square-well-complete-bound-state-energy-normalized-wavefunctions?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need the exact, fully normalized quantum mechanical solution for a finite symmetric square well — including all bound states and their spatial wavefunctions at arbitrary positions — rather than the infinite-well approximation or a purely numerical grid simulation. It is ideal for semiconductor device design, optical transition calculations, and physics education where analytical accuracy and normalized eigenstates are required.
Side effects
- Well parameters that support no bound states (very shallow or narrow well) may return an empty spectrum
- Query positions outside the numerical domain may produce edge artifacts
- mass_ratio or depth_ev at boundary extremes may cause solver convergence issues
- Malformed or missing required fields return a 400 validation error
- Too many query positions (>8) rejected with schema validation error
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| artifact | object |
Tags
x402
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