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Add Classical and Quantum Hamiltonian functions to physics algorithms #13235

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enhancementThis PR modified some existing files
@morgen-code

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@morgen-code

Feature description

I would like to suggest adding functions for the Hamiltonian in both classical mechanics and quantum mechanics
to thephysics directory.

Proposed functions

  1. Classical Hamiltonian
    Computes H = T + V for a particle or system, where T is kinetic energy and V is potential energy.
    Example use case: free particle, harmonic oscillator, simple pendulum.

  2. Quantum Hamiltonian (1D)
    Constructs the Hamiltonian matrix for a particle in a 1D potential using finite difference discretization.
    Example use case: solving the time-independent Schrödinger equation.

Benefits

Provides a practical way for learners to understand and simulate physical systems in Python.
Fits the existing educational purpose of thephysics directory as a collection of algorithmic implementations.

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