Scientific Coding

Quantum Physics 2026

Schrödinger Equation Solver

Numerical solution of the time-independent Schrödinger equation for various potential wells using finite difference methods.

Python NumPy SciPy Matplotlib

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import numpy as np
from scipy import linalg
# Harmonic oscillator V = ½x²
N  = 1000
x  = np.linspace(-10, 10, N)
dx = x[1] - x[0]
V  = 0.5 * x**2
d  = np.ones(N) / dx**2 + V
o  = -0.5 * np.ones(N-1) / dx**2
H  = np.diag(d) + np.diag(o,1) + np.diag(o,-1)
E, ψ = linalg.eigh(H)
        

Data Analysis 2026

Paschen's Law Verification

Data analysis pipeline for the experimental verification of Paschen's law. Includes curve fitting and uncertainty propagation from electrical discharge measurements.

Python Pandas SciPy

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from scipy.optimize import curve_fit
import numpy as np

def paschen(pd, A, B, g):
    t = np.log(1 + 1/g)
    return B*pd / (np.log(A*pd) - np.log(t))

popt, pcov = curve_fit(
    paschen, df["pd"], df["Vb"],
    p0=[12, 365, 0.01]
)
err = np.sqrt(np.diag(pcov))
        

Machine Learning 2025

Neural Network for Phase Classification

Fully connected neural network classifying phases of matter from thermodynamic state vectors, trained on Monte Carlo simulations of the Ising model.

Python PyTorch Scikit-learn

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import torch.nn as nn

class PhaseNet(nn.Module):
  def __init__(self):
    super().__init__()
    self.net = nn.Sequential(
      nn.Linear(4,64), nn.ReLU(),
      nn.Linear(64,64), nn.ReLU(),
      nn.Linear(64,4),
    )
  def forward(self,x):
    return self.net(x)
        

Schrödinger Equation Solver

Paschen's Law Verification

Neural Network for Phase Classification