What is a Hamiltonian? Quantum Jargon Explained

In this series we define common quantum terminology.
This episode of Quantum Jargon: Hamiltonian.
In quantum mechanics, a hamiltonian is a mathematical description of the total energy of a system, incorporating both kinetic and potential energy.
The system being described could be anything: a molecule, a single qubit, or a bouncy ball.
A hamiltonian can take different forms, it might incorporate different types of energy contributions, or be written in different coordinates or dimensions, which often makes them look very different.
In quantum mechanics, knowing the Hamiltonian of your system is very important, because it will allow you to solve the Schrodinger Equation; the heart of quantum mechanics.
The Schrodinger Equation calculates how the system will evolve or change in time, which tells us basically everything useful we would want to know.
That is why the first step of almost any problem or experiment boils down to calculating or identifying the Hamiltonian.

[@ardiris2715]

As an educator, I like this format.

[@mohammadrashikzaman3001]

Shortest but smartest definition.

[@Handelsbilanzdefizit]

Wondering, if you put into hamiltonoperator the gravitational potential of a very very tiny black hole, would the nearby electrons also arrange in shells?
And would these black-hole-atoms build up molecules? What sort of heavy-matter would that be? And would it interact with light and radiation? 🤔

[@rigobertovillalobos3614]

"Power of the universes, powers of creation "

[@m.matoori343]

Thanks

[@geneyoung11111]

Omission of this important elements for H.
$ \int \mathcal{L}(q, q’, t) dt, \int \eta(x)f(x) = 0 $ for understanding euler equation derivation.
\delta s = \delta \int L dt = 0, p \equiv \frac{\partial \mathcal{L}}{\partial q’}, H = \sum pq’ - \mathcal {L} for Hamiltonian.

[@ayush6722]

All right! Video could've been a little more longer haha

[@WilliamDye-willdye]

I like it short. Sometimes I just need to remind myself of a quick definition. If I want more I can go elsewhere.

[@douglasgoldfarb3421]

Mit and design teams in artificial intelligence sentient

[@highdry6646]

*Kinetial Energy*

[@Randomsena0007]

My audience watches this 😂

[@patearth]

I do not love when you talk about quantum and use only classical movements in the video

[@douglasgoldfarb3421]

Artificial intelligence sentient systems working through usnorthcom military and cory bear tandon engineering nyu metrotech