Pauli Exclusion Principle rendered as python code : Tomachi Corporation

Can the Pauli Exclusion Principle be expressed as pseudo-code for the first dozen elements?

The Pauli Exclusion Principle can be represented cleanly in code as a uniqueness constraint. The principle dictates that no two identical fermions (like electrons) can occupy the exact same quantum state simultaneously.

The Core Logic (Pseudo-code)

In quantum mechanics, an electron’s state is defined by a unique combination of four quantum numbers: [1]

1. Principal quantum number (n)
2. Orbital angular momentum (l)
3. Magnetic quantum number (m_l)
4. Spin quantum number (m_s)

The entire Pauli Exclusion Principle can be summarized in a single algorithmic rule: The collection of electron states must be a Set (where duplicates are impossible), not a List. [1, 2, 3]

python

# Rule: Two electrons cannot have the same 4 quantum numbers
def validate_pauli_exclusion(atom_electron_cloud):
    # A set only stores unique tuples
    unique_states = set(atom_electron_cloud)
    
    # If the lengths don't match, a duplicate quantum state was attempted
    if len(unique_states) != len(atom_electron_cloud):
        return "Error: Pauli Exclusion Principle Violated!"
    return "Valid Element Configuration"

Simulating the First Dozen Elements

Below is a complete script demonstrating how the code populates the electron shells sequentially for the first 12 elements (Hydrogen through Magnesium), strictly enforcing the rule that each state tuple (n, l, m_l, m_s) must be entirely unique. [1]

python

# Define the available quantum states in order of increasing energy (Aufbau principle)
# Format: (n, l, m_l, m_s)
AVAILABLE_STATES = [
    # 1s shell (Capacity: 2)
    (1, 0, 0, +0.5), (1, 0, 0, -0.5),
    
    # 2s shell (Capacity: 2)
    (2, 0, 0, +0.5), (2, 0, 0, -0.5),
    
    # 2p shell (Capacity: 6)
    (2, 1, -1, +0.5), (2, 1, -1, -0.5),
    (2, 1,  0, +0.5), (2, 1,  0, -0.5),
    (2, 1,  1, +0.5), (2, 1,  1, -0.5),
    
    # 3s shell (Capacity: 2)
    (3, 0, 0, +0.5), (3, 0, 0, -0.5)
]

ELEMENTS = [
    "Hydrogen", "Helium", "Lithium", "Beryllium", "Boron", "Carbon", 
    "Nitrogen", "Oxygen", "Fluorine", "Neon", "Sodium", "Magnesium"
]

def build_element_electron_cloud(atomic_number):
    electron_cloud = []
    
    for i in range(atomic_number):
        next_quantum_state = AVAILABLE_STATES[i]
        
        # Pseudo-code check for Pauli Exclusion Principle before adding
        if next_quantum_state in electron_cloud:
            raise Exception("Quantum state already occupied!")
            
        electron_cloud.append(next_quantum_state)
        
    return electron_cloud

# Outputting the configurations for the first 12 elements
for index, name in enumerate(ELEMENTS):
    atomic_number = index + 1
    cloud = build_element_electron_cloud(atomic_number)
    print(f"{name} (Z={atomic_number}): {len(cloud)} electrons allocated uniquely.")

Version 1, 2, and 3

Version 3 is the latest. other versions. It has some issues, so some planned improvements when my free-tier credits resume:

Charged free particles like protons / electrons should attract/repel each other strongly, then go neutral when together in atom
Free neutrons can show gravitational clumping together but should spread out if no protons are nearby into a neutron mist acting more like bowling balls kinetically bouncing away from negative charges if they hit each other
When a neutron hits a proton it forms a Helium nucleus
Once an atom is formed its charge state determines its attraction or repulsion with other particles which can stop processing attraction
Once a molecule is formed its charge state determines its attractions with other particles and it’s constituent atoms can stop processing attraction repulsion
The electron animation needs a full rewrite, suggest a pixel shader which is like a mist or jelly and takes into account the number of electrons present and optimizes by rendering only the outer 1 or 2 orbital layers for speed

Simulating the First Dozen Elements

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