Source: https://guthlabs.ai/docs/instruments/de-broglie-wavelength-calculator/mechanism/

instrument mechanism / verified-clean

# de Broglie Wavelength Calculator mechanism

The inspectable method record for de Broglie Wavelength Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The core non-relativistic and momentum forms are standard and numerically testable. Verdict is NEEDS_REVIEW because the relativistic option and the atomic-scale comparison are not mathematically specified, and the honest label does not identify the actual relativistic equations or input constraints.

- λ=h/p is the standard de Broglie relation when p is momentum, and λ=h/(mv) is correct only in the non-relativistic approximation p=mv.

- The claimed relativistic option is underspecified: no relativistic momentum formula or kinetic-energy-to-momentum formula is provided. For relativistic velocity, p=γmv with γ=1/sqrt(1-v²/c²); for relativistic kinetic energy K, p=sqrt(((K/c)+mc)^2-(mc)^2), equivalently p=sqrt(K²/c²+2mK).

- The output claim 'comparison to atomic scale' has no defined reference length or comparison formula, so that output cannot be verified.

## Units and conventions

- h=6.62607015e-34 J·s exactly.

- Mass must be supplied in kilograms, momentum in kg·m/s, velocity in m/s, kinetic energy in joules, and wavelength is returned in meters.

- The mass presets are assumed to use electron mass 9.1093837e-31 kg, proton mass 1.67262192369e-27 kg, and neutron mass in kilograms.

- The velocity formula λ=h/(mv) assumes non-relativistic motion, sufficiently far below the speed of light.

- If atomic-scale comparison is implemented, its reference scale must be explicitly specified, for example 1e-10 m; no such assumption is made here.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "mode": "velocity",
    "particle": "electron",
    "mass_kg": 9.1093837e-31,
    "velocity_m_per_s": 1000000,
    "h_J_s": 6.62607015e-34
  },
  "expected_outputs": {
    "wavelength_m": 7.2738951e-10
  },
  "working": "p=mv=(9.1093837e-31 kg)(1.000000e6 m/s)=9.1093837e-25 kg·m/s. λ=h/p=(6.62607015e-34 J·s)/(9.1093837e-25 kg·m/s)=0.72738951e-9 m=7.2738951e-10 m."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The specification leaves hazardous edge behavior unresolved: zero momentum causes division by zero, v=c is outside the non-relativistic model although plain arithmetic produces a value, and signed velocity can produce a negative wavelength unless magnitude and direction conventions are separated.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/de-broglie-wavelength-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/de-broglie-wavelength-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/de-broglie-wavelength-calculator/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`