Introduction to Pandas for Physics: Data Transformation, Filtering & Physical Slicing - Computational Physics Formulation & Simulation

Program 1

Data Transformation, Filtering & Physical Slicing

Python 3.11 Ready

import pandas as pd
import numpy as np

# Fundamental physical constants
e_charge = 1.60217663e-19  # Electron charge (Coulombs)
c_speed  = 2.99792458e8    # Speed of light (m/s)

# Trial 1: Cesium Cathode (Work Function Phi ~ 2.14 eV)
cesium_data = {
    'wavelength_nm': [650.0, 589.0, 546.0, 436.0, 405.0, 365.0],
    'stopping_potential_V': [0.00, 0.21, 0.45, 1.15, 1.42, 1.88],
    'cathode_material': ['Cesium'] * 6
}

# Trial 2: Potassium Cathode (Work Function Phi ~ 2.29 eV)
potassium_data = {
    'wavelength_nm': [600.0, 546.0, 436.0, 405.0, 365.0],
    'stopping_potential_V': [0.00, 0.32, 1.02, 1.28, 1.73],
    'cathode_material': ['Potassium'] * 5
}

df_cs = pd.DataFrame(cesium_data)
df_k  = pd.DataFrame(potassium_data)

# 1. Concatenate datasets into a unified experimental DataFrame
df_photo = pd.concat([df_cs, df_k], ignore_index=True)

# 2. Derived Physical Quantities: Frequency nu = c / lambda
df_photo['frequency_THz'] = (c_speed / (df_photo['wavelength_nm'] * 1e-9)) * 1e-12

# Maximum kinetic energy: K_max = e * V_0 (eV)
df_photo['K_max_eV'] = df_photo['stopping_potential_V']

# 3. Physical Filtering: Isolate active photoemission regime (V_0 > 0)
df_active = df_photo[df_photo['stopping_potential_V'] > 0.0].copy()

# 4. Multi-Condition Slicing: Ultraviolet region (lambda < 450 nm) for Cesium
df_uv_cs = df_photo[(df_photo['cathode_material'] == 'Cesium') & (df_photo['wavelength_nm'] < 450.0)]

print("=== Complete Photoelectric Experiment Ledger ===")
print(df_photo.head(6))

# Sort active regime by cathode material and frequency
df_sorted = df_active.sort_values(by=['cathode_material', 'frequency_THz'], ascending=[True, True])
print("\n=== Active Emission Regime (V_0 > 0) Sorted by Frequency ===")
print(df_sorted[['cathode_material', 'wavelength_nm', 'frequency_THz', 'stopping_potential_V', 'K_max_eV']].to_string(index=False))

# 5. Calculate Experimental Planck's Constant: h = e * (Delta V0 / Delta nu)
cs_trials = df_active[df_active['cathode_material'] == 'Cesium']
delta_V = cs_trials['stopping_potential_V'].iloc[-1] - cs_trials['stopping_potential_V'].iloc[0]
delta_nu = (cs_trials['frequency_THz'].iloc[-1] - cs_trials['frequency_THz'].iloc[0]) * 1e12
h_exp = e_charge * (delta_V / delta_nu)

h_accepted = 6.62607015e-34
pct_err = abs(h_exp - h_accepted) / h_accepted * 100.0

print(f"\nCalculated Planck's Constant: h = {h_exp:.3e} J*s (Accepted: {h_accepted:.3e} J*s, Error: {pct_err:.2f}%)")

Click "Run Code" to execute script and render figures.

Mathematical Problem Formulation

Physical Law: Einstein's Photoelectric Equation:

When monochromatic light of frequency $\nu = \frac{c}{\lambda}$ strikes a photocathode, the maximum kinetic energy $K_{\text{max}}$ of emitted photoelectrons is given by Einstein's relation:

$$K_{\text{max}} = e V_0 = h \nu - \Phi$$

where $V_0$ is the stopping potential (in Volts), $e$ is the elementary charge ($1.602 \times 10^{-19}\,\text{C}$), $h$ is Planck's constant, and $\Phi$ is the work function of the material.

Condition for Active Photoelectric Emission:

Photoemission occurs exclusively when photon energy exceeds the work function:

$$h \nu > \Phi \iff V_0 > 0$$

The slope of stopping potential versus optical frequency yields Planck's constant:

$$\frac{dV_0}{d\nu} = \frac{h}{e} \implies h = e \left( \frac{\Delta V_0}{\Delta \nu} \right)$$

Theoretical Background & Computational Mechanics

1. Filtering & Relational Slicing in Experimental Physics:

Physical experiments often encompass multiple regimes (e.g., sub-threshold non-emission vs above-threshold photoemission). Pandas enables instantaneous filtering using boolean conditions (such as df[df['stopping_potential_V'] > 0]) without mutating original records.

2. Multi-Dataset Merging & Concatenation:

In experimental laboratories, measurements on different materials (e.g., Cesium vs Potassium cathodes) are often logged in separate trials. pd.concat() unifies them into a comprehensive comparative ledger, while .sort_values() organizes them monotonically by frequency.

3. Derivation of Fundamental Physical Constants:

By extracting active rows from the filtered DataFrame and computing differential ratios $\frac{\Delta V_0}{\Delta \nu}$, students determine experimental values of Planck's constant $h$ directly from laboratory data.

Theoretical Principles & Computational Physics Guide

Data Transformation, Filtering & Physical Slicing: Computational Physics Modeling & Analysis

Dr. Alorika Chatterjee & Dr. Anirban Shaw Science & Physics Learners Python 3 / NumPy / SciPy

1. Core Principles & Theoretical Framework

Core Concept: Computational formulation and simulation of Data Transformation, Filtering & Physical Slicing within the study of Introduction to Pandas for Physics.

Algorithmic Translation: Translates theoretical governing equations into clean, discrete Python procedures and verified numerical solvers.

Numerical Verification: Evaluates numerical accuracy, parameter sensitivity, and error bounds for reliable computational results.

2. Mathematical Formulation & Algorithmic Pipeline

Governing computational formulation for Data Transformation, Filtering & Physical Slicing:

$$ \mathcal{F}_{\text{model}}(\mathbf{x}, t; \mathbf{p}) = 0 \implies \mathbf{y}_{n+1} = \mathcal{S}(\mathbf{y}_n, \Delta t, \mathbf{p}) $$

1. Define Physical Parameters & Boundaries → 2. Execute Numerical Simulation Steps → 3. Evaluate Observables & Plot Results

3. Numerical Mechanics & Implementation Logic

Parameter Initialization: Set physical constants, initial states, and coordinate boundary bounds for Data Transformation, Filtering & Physical Slicing.
Step Execution: Advance the computational state using optimized vector operations and scientific libraries.
Convergence Control: Monitor stability and ensure simulation metrics remain physically meaningful.

4. Relevant Computational Practice Exercises

Exercise 1

Implement Data Transformation, Filtering & Physical Slicing and observe how the output responds to variations in primary physical parameters.

Exercise 2

Refine the calculation grid or step size to observe convergence and reduction in numerical approximation error.

Exercise 3

Compare the simulated computational results against an analytical benchmark or limiting physical case.

Standard Literature & References:

Mark Newman, "Computational Physics", University of Michigan (2013).
Hans Petter Langtangen, "A Primer on Scientific Programming with Python", Springer (2016).

Ch. 8.5 Data Transformation, Filtering & Physical Slicing