{"uid":"cap_PpXlG9mjsLIrY8W9reta7","slug":"finite-square-well-complete-bound-state-energy-normalized-wavefunctions-05fa444c","name":"Finite Square Well Complete Bound State Energy & Normalized Wavefunctions","description":"Recover the complete discrete spectrum and normalized spatial states of an explicit finite quantum well.","url":"https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B009/finite-square-well-complete-bound-state-energy-normalized-wavefunctions?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["quantumWell"],"properties":{"quantumWell":{"type":"object","required":["data","claim"],"properties":{"data":{"type":"object","required":["half_width_nanometers","mass_ratio","depth_ev","query_positions_nanometers"],"properties":{"depth_ev":{"type":"number","maximum":1000,"minimum":0.001},"mass_ratio":{"type":"number","maximum":10,"minimum":0.01},"half_width_nanometers":{"type":"number","maximum":1000,"minimum":0.01},"query_positions_nanometers":{"type":"array","items":{"type":"number","maximum":10000,"minimum":-10000},"maxItems":8,"minItems":1}},"additionalProperties":false},"claim":{}},"additionalProperties":false}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_kpprlevn318EqnE7wQ_Iu","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"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.","exampleAgentPrompt":"Solve the complete bound-state spectrum for a finite square quantum well that is 5 nm half-width, 0.3 eV deep, with an effective mass ratio of 0.067, and evaluate the normalized wavefunctions at positions -6, -3, 0, 3, and 6 nanometers.","exampleUseCases":[{"title":"Semiconductor quantum well energy levels","prompt":"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?"},{"title":"Nanoscale confinement physics homework","prompt":"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."},{"title":"Quantum well wavefunction overlap integral","prompt":"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."}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:38:43.930Z","isFirstParty":false,"canonicalSlug":"finite-square-well-complete-bound-state-energy-normalized-wavefunctions-05fa444c"}