In quantum mechanics, quantum chemistry, and condensed matter physics courses, it seems like finding the ground state energy of a Hamiltonian is incredibly important. I can understand why having the ground state wave function (or behaviors of the wave function) could help, but I’m struggling to understand how the ground state energy helps us.

In Quantum Computing pitches by huge companies, I always hear something along the lines of “Quantum Chemistry simulations will allow for breakthroughs in the pharmaceutical industries,” but the quantum simulation algorithm in quantum computing they refer to is the Variational Quantum Eigensolver, which returns an estimate for the ground state energy. How does knowing this energy tell us anything about the material? I’m struggling to bridge this gap.

  • $\begingroup$ To understand the excited states, you need to understand the ground state. If you can't get the ground state correct, why would you believe any excited states? $\endgroup$ – Jon Custer Jun 10 at 19:47
  • $\begingroup$ I can understand this argument for the states themselves, but does the ground state energy on it's own tell us anything? $\endgroup$ – Jlee523 Jun 10 at 22:11
  • $\begingroup$ DFT for narrow-gap semiconductors quite often results in a ground state with a negative band gap - that is, DFT says it is a metal. So, how do you trust any DFT results on the material? Well, you don't until you get a proper ground state. In other situations, what you 'know' the ground state to be might not be what it actually is, particularly for complex systems with long range interactions. $\endgroup$ – Jon Custer Jun 10 at 23:13
  • $\begingroup$ So is the claim that knowing the GS energy tells us nothing, other than the fact that we can use the results to check against our other calculations? As in, knowing the true GS allows us to use and trust other computational methods? $\endgroup$ – Jlee523 Jun 10 at 23:26

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