# Finite Square Well Complete Bound State Energy & Normalized Wavefunctions

> 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.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B009/finite-square-well-complete-bound-state-energy-normalized-wavefunctions?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-04
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/finite-square-well-complete-bound-state-energy-normalized-wavefunctions-05fa444c
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_PpXlG9mjsLIrY8W9reta7

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability finite-square-well-complete-bound-state-energy-normalized-wavefunctions-05fa444c -d '<json body>'
```

Example prompt: 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.

## When to prefer this

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.

## Known failure modes

- 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

## 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.

## Request schema (JSON Schema)

```json
{
 "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
  }
 }
}
```

## More

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