Add Classical and Quantum Hamiltonian functions to physics algorithms

[morgen-code]

Feature description

I would like to suggest adding functions for the Hamiltonian in both classical mechanics and quantum mechanics
to the physics 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 the physics directory as a collection of algorithmic implementations.

[devx099]

Hello, I’m Dev
I would like to work on this issue as part of Hacktoberfest. This would be my first open-source contribution.
And I will really appreciate any advice or guidance you might have for me. or you can specify more if you can.
Could you please assign this issue to me so I can start working on it?

[morgen-code]

Hi Dev (@devx099 )
That’s great to hear. Thank you for your interest in working on this issue.

Yes, please go ahead and start working on it.

Here’s a suggested structure:

• classical_hamiltonian(m, p, V) → returns p**2 / (2*m) + V
• quantum_hamiltonian_1d(m, hbar, V, dx) → builds the Hamiltonian matrix using the finite difference method.
  • Note: hbar is included as an input parameter to allow flexible choice of unit systems (e.g., natural units or SI units).

Let me know if you have any questions or would like feedback while implementing.
I’ll be happy to help.

[pipineitor]

Hello, I’m Dev
I would like to work on this issue as part of Hacktoberfest. This would be my first open-source contribution.
And I will really appreciate any advice or guidance you might have for me. or you can specify more if you can.
Could you please assign this issue to me so I can start working on it?

My number is +58 4168068615 wsp