ScienceShot science reference

Quantum tunnelling through a rectangular barrier

quantum_tunnelling

Read-onlyIdempotent

Calculate the exact transmission coefficient of a one-dimensional rectangular potential barrier for an electron, proton or alpha particle, below or above the barrier height. Give particle energy and barrier height in eV and barrier width in nm; the result adds the WKB exponential estimate, the thick-barrier asymptote and the decay length. Textbook closed form (OpenStax University Physics 3, 7.6) with CODATA 2018 masses; a single square barrier only, no band structure or image-charge effects.

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "particle": "<particle>",
      "energy_ev": "<energy_ev>",
      "height_ev": "<height_ev>",
      "width_nm": "<width_nm>"
    },
    "name": "quantum_tunnelling"
  }
}

Input Schema

Name	Required	Description
`particle`	Yes
`width_nm`	Yes	Barrier width in nm, 0 or more.
`energy_ev`	Yes	Particle kinetic energy in eV, greater than 0.
`height_ev`	Yes	Barrier height in eV, greater than 0.

Schema Changelog

Changes observed during successful MCP inspections.

First observedNov 7, 2026

TDQS

A4.4/5.0

Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already cover the safety profile (read-only, idempotent, non-destructive, closed-world), so the description's added value is in disclosing the physics model, unit conventions, source (OpenStax, CODATA 2018 masses) and the extra outputs bundled with the result. That is genuinely useful context beyond the annotations; only numerical-precision or limit behavior at E = height is unstated.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Two dense sentences, front-loaded with the operation and resource, followed by units, return contents and model limitations. Every clause carries information an agent needs; nothing repeats the schema verbatim.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With no output schema, the description correctly enumerates what the result contains (transmission coefficient, WKB estimate, thick-barrier asymptote, decay length), and it pins down units and model limitations. The only gap for a four-parameter physics calculator is unstated edge-case behavior near E = barrier height or zero width.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters4/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 75% with units and ranges already documented per parameter, and the description adds the governing convention that energy and height are both in eV and width in nm. It also clarifies that energy may lie below or above the barrier height, which is semantically important and not obvious from the schema alone.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb and resource ('Calculate the exact transmission coefficient of a one-dimensional rectangular potential barrier') and immediately narrows the domain to electron/proton/alpha and energies below or above the barrier height. No sibling tool covers tunnelling, and the description makes that distinct physics scope unmistakable.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Gives clear context for use (single square barrier, above or below barrier height) and explicit exclusions ('no band structure or image-charge effects'), which tells the agent when this model does not apply. It does not name an alternative tool, but no sibling covers the same ground, so the only missing piece is minor.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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