Theoretical Principles & Computational Physics Guide
Conditionals (if, elif, else): Logical Branching & Piecewise Physical Laws
Dr. Alorika Chatterjee & Dr. Anirban Shaw
Science & Physics Learners
Python 3 / NumPy / SciPy
1. Core Principles & Theoretical Framework
Piecewise Physics: Models potential energy wells, elastic wall collisions, and threshold phase transitions.
Relational Checks: Evaluates state conditions using relational ($<, >, ==, \neq$) and boolean operators (
and, or, not). Boundary Handling: Detects spatial domain boundaries to reflect velocities or apply absorbing conditions.
2. Mathematical Formulation & Algorithmic Pipeline
Piecewise 1D finite potential well formulation:
$$ V(x) = \begin{cases} 0, & |x| < a \ V_0, & |x| \ge a \end{cases} \quad \implies \quad \texttt{V = 0.0 if abs(x) < a else V0} $$
3. Numerical Mechanics & Implementation Logic
- Threshold Branching: Route computation to appropriate analytical or numerical regime based on physical parameters.
- Elastic Reflection: Invert velocity ($v \leftarrow -v$) when particle coordinate crosses boundary $x \le 0$ or $x \ge L$.
- Short-Circuit Evaluation: Structure compound conditions so computationally lightweight checks run before expensive functions.
4. Relevant Computational Practice Exercises
Exercise 1
Compute the electric potential $V(r)$ of a uniformly charged sphere of radius $R$ inside ($r < R$) and outside ($r \ge R$).
Exercise 2
Classify roots of a quadratic equation $ax^2 + bx + c = 0$ into real distinct, degenerate, or complex conjugate roots.
Exercise 3
Simulate an elastic bouncing ball under gravity, reversing velocity with a restitution coefficient upon impact with $y = 0$.
- Mark Newman, "Computational Physics", University of Michigan (2013).