this post was submitted on 19 Aug 2025
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Explain Like I'm Five

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ELI5: what is a quantum state? (lemmy.world)
submitted 8 months ago by rtxn@lemmy.world to c/explainlikeimfive@lemmy.world
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I've been reading a lot about massive stellar objects, degenerate matter, and how the Pauli exclusion principle works at that scale. One thing I don't understand is what it means for two particles to occupy the same quantum state, or what a quantum state really is.

My background in computers probably isn't helping either. When I think of what "state" means, I imagine a class or a structure. It has a spin field, an energy_level field, and whatever else is required by the model. Two such instances would be indistinguishable if all of their properties were equal. Is this in any way relevant to what a quantum state is, or should I completely abandon this idea?

How many properties does it take to describe, for example, an electron? What kind of precision does it take to tell whether the two states are identical?

Is it even possible to explain it in an intuitive manner?

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[–] CanadaPlus 1 points 8 months ago* (last edited 8 months ago) (1 children)

Is this calculated by assuming the wavefunction is static? Like, maybe a steady-state eigenfunction of the system's evolution with an eigenvalue that's 1, or another root of unity.

[–] FrenziedFelidFanatic@pawb.social 1 points 8 months ago

Is this calculated by assuming the wavefunction is static?

Typically sorta? The way the Schrödinger equation is typically solved is by taking linear combinations of eigenfunctions (of the Hamiltonian) and making them time-dependent with a time-dependent phase out front.

The eigenfunctions are otherwise time-independent since you can usually make the Hamiltonian be time independent.

If the problem is easier to think about with a time-dependent Hamiltonian, you can use the Heisenberg formulation of quantum mechanics, which makes the wavefunctions static and lets the operators evolve in time. This can be helpful in a number of situations—typically involving light.

Like, maybe a steady-state eigenfunction of the system's evolution with an eigenvalue that's 1, or another root of unity.

I assume you mean eigenfunction of the Hamiltonian here, but the eigenvalue associated with that eigenfunction would be the energy of the state, so you can’t really make it be a root of unity (it must, in fact, be fully real since energy is an observable)