# Quantum Mechanics Energy Levels AI Agent Connect

> Calculate energy eigenvalues, wavefunctions, and probability densities for fundamental quantum models.

## Overview
- **Category:** science
- **Price:** Free
- **Endpoint:** https://edge.vinkius.com/vk_preview_9JcVxfDoSnWLctWgC8USFtZDbzNIuhZHLbiBt24Z/ai-agent-connect
- **Tags:** quantum, schrodinger, physics-engine, wavefunction, eigenvalues

## Description

This MCP server provides computational tools for solving the time-independent Schrödinger equation for key quantum mechanical systems. It allows AI agents to determine energy eigenvalues, wavefunctions, and probability distributions for the Infinite Square Well, the Quantum Harmonic Oscillator, and the Hydrogen Atom. Use `calculate_particle_in_box` for 1D potential wells, `calculate_harmonic_oscillator` for restorative force models, and `calculate_hydrogen_atom` for atomic orbital properties. You can also use `get_quantum_state_summary` to receive qualitative descriptions of specific quantum states.

## Tools

### calculate_harmonic_oscillator
Calculates energy and spatial properties for a quantum harmonic oscillator

### calculate_hydrogen_atom
Calculates energy and orbital properties for a hydrogen-like atom

### calculate_particle_in_box
Calculates the properties of a particle trapped in a 1D infinite potential well

### get_quantum_state_summary
Provides a qualitative description of the particle's state based on its quantum numbers

## Prompt Examples

**Prompt:** 
```
What is the energy of a particle in a box with width 1.0 and quantum number 1?
```

**Response:** 
```
The energy eigenvalue for a particle in a box with width 1.0 and n=1 is approximately 5.67e-18 Joules.
```

**Prompt:** 
```
Calculate the energy for a harmonic oscillator with frequency 100 and quantum number 0.
```

**Response:** 
```
The energy for the ground state (n=0) of a harmonic oscillator with frequency 100 is 50.0.
```

**Prompt:** 
```
What is the radial probability density for a hydrogen atom with n=2, l=1, ml=0 at r=0.5?
```

**Response:** 
```
The radial probability density at r=0.5 for the specified hydrogen atom state is 0.125.
```

## Frequently Asked Questions

**What quantum models are supported?**
The server supports the Infinite Square Well (Particle in a Box), the Quantum Harmonic Oscillator, and the Hydrogen Atom.

**How do I get a description of a specific state?**
You can use the `get_quantum_state_summary` tool to get a qualitative description like 'Ground State' and an energy tier classification.

**Can I calculate probability density?**
Yes, tools like `calculate_particle_in_box` and `calculate_harmonic_oscillator` return the probability density at specific coordinates.