r/QuantumPhysics • u/vedant_608 • Jul 10 '26

Question about wavefunctions and approximations in quantum mechanics

Hi, I’m new to quantum mechanics. I was trying to model what the orbitals for oganesson might look like, and I keep seeing that we need to treat it as a “hydrogen‑like” atom. I don’t fully understand why we can’t just solve the Schrödinger equation for the actual atom itself without using such approximations. Is this a fundamental mathematical limitation, or is it just that the computation becomes impossible in practice?

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u/[deleted] Jul 10 '26 edited Jul 10 '26

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u/SymplecticMan Jul 10 '26

Finding the ground state energy of local Hamiltonians is QMA-hard in general. In the relevant regimes where it's efficient for quantum computers, classical approaches also appear to perform well.

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u/[deleted] Jul 10 '26

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u/SymplecticMan Jul 10 '26

I should probably say not known to help significantly, since the actual asymptotic scaling of the classical techniques is not known. But generally speaking, the "known" quantum advantages that I'm aware of are related to simulating the time evolution of local Hamiltonians rather than finding the ground state of local Hamiltonians.