# Particle in a Box Calculator AI Agent Connect

> Simulate quantum mechanics for particles in 1D, 2D, and 3D rigid potential wells.

## Overview
- **Category:** science
- **Price:** Free
- **Endpoint:** https://edge.vinkius.com/vk_preview_iqYzYIu4zYs9peFqh7lAHmw2S7Jd84VHNnMJ3sCA/ai-agent-connect
- **Tags:** quantum-mechanics, physics-simulation, wavefunction, energy-levels, particle-physics

## Description

This MCP server provides tools to solve fundamental quantum mechanics problems for particles confined in rigid potential wells. You can use `calculate_energy_state` to find discrete energy levels, `get_wavefunction_amplitude` to find the wavefunction value at specific coordinates, `get_probability_density` to determine the likelihood of finding a particle at a point, and `list_energy_spectrum` to view a range of available energy states. It supports 1D, 2D, and 3D configurations.

## Tools

### calculate_energy_state
Determines the specific energy level for a particle in a given box dimension and state

### get_probability_density
Calculates the probability density at a specific point in space

### get_wavefunction_amplitude
Calculates the value of the wavefunction at a specific spatial coordinate

### list_energy_spectrum
Provides a range of available energy levels for a particle within a specific box configuration

## Prompt Examples

**Prompt:** 
```
What is the energy level for an electron in a 1D box of 1nm length with n=1?
```

**Response:** 
```
The energy level for an electron in a 1nm 1D box at n=1 is approximately 6.025e-19 Joules.
```

**Prompt:** 
```
Calculate the probability density at x=0.5 for a 1D box of 1m length, mass 1kg, n=1.
```

**Response:** 
```
The probability density at x=0.5 is 0.4 Joules/m^2.
```

**Prompt:** 
```
List the first few energy levels for a 2D box with Lx=1, Ly=1, mass=1, up to n=2.
```

**Response:** 
```
The energy levels are: nx=1, ny=1: 1.0; nx=1, ny=2: 2.0; nx=2, ny=1: 2.0; nx=2, ny=2: 4.0.
```

## Frequently Asked Questions

**What dimensions are supported?**
The server supports 1D, 2D, and 3D rigid potential wells.

**How do I find the energy of a specific state?**
Use the `calculate_energy_state` tool by providing the dimension, box dimensions, particle mass, and quantum numbers.

**Can I see multiple energy levels at once?**
Yes, you can use `list_energy_spectrum` to retrieve a range of energy levels up to a specified maximum quantum number.