What is hamiltonian?

Hi everyone, I am trying to understand Hamiltonian. This term is mentioned in lot of papers. Can you explain me what exactly is Hamiltonian and what exactly is its use?
Any help

Hey @Manu_Chaudhary, great question! A Hamiltonian describes the interactions of degrees of freedom (e.g., particles, qubits, electrons, etc.) with themselves and their environment. Each term in a Hamiltonian describes a particular type of interaction. In quantum mechanics, the Hamiltonian is an operator with eigenvalues that represent the energy of the corresponding eigenstate. It’s the foundation of the Schrodinger’s equation for how quantum states evolve over time!

That’s the very brief answer to your question, and I definitely recommend supplementing my answer with some independent studying :slight_smile:. I can recommend these two textbooks:

  • “Principles of Quantum Mechanics” by R. Shankar:
  • “Modern Quantum Mechanics” by J. J. Sakurai and Jim Napolitano:

Let me know if that helps!