Scientific Coding – Heelyess Tahiri

Quantum Physics2026

Schrödinger Equation Solver

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

PythonNumPySciPyMatplotlib

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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 Analysis2026

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.

PythonPandasSciPy

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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 Learning2025

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.

PythonPyTorchScikit-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)
        