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> Furthermore, plenty of physicists don't actually grasp the fundamentals of their own field I once met a professor at a quantum chemistry conference who argue
by Xcelerate 10y ago
> Furthermore, plenty of physicists don't actually grasp the fundamentals of their own field
I once met a professor at a quantum chemistry conference who argued with me that I could not converge on the exact eigenvalues of a helium atom (assuming a simplified Hamiltonian with a few Coulombic terms). He stated the oft repeated mantra that "the Schrödinger equation can't be solved for any element other than hydrogen", so I wrote a program that brute force diagonalized the Hamiltonian to demonstrate otherwise. He was confusing the notion of a closed-form solution (an analytical expression that gives the solution in terms of specified elementary functions) with that of a numerically exact solution (one that converges on the exact solution but can't be expressed in terms of specified elementary functions).
Another professor who was teaching a course on statistical mechanics once said that the single particle wave function is more fundamental than the multi-particle wave function. Nevermind the fact that his research involved density functional theory, which famously fails on those cases where the molecular wave function can't be well approximated using a product of single particle wave functions.
- codethief 10y ago> Another professor […] once said that the single particle wave function is more fundamental than the multi-particle wave function. Nevermind […] his research […] where the molecular wave function can't be well approximated using a product of single particle wave functions Depends on what you mean by "multi-particle wave function". The way it is usually understood (I think), it includes all possible tensor products of single-particle wave functions. Then it should be possible, shouldn't it?
- monktastic1 10y agoTensor products only describe the separable (i.e., unentangled) states.
- tomonl 10y agoAs I understand it, that is only true when dealing with density matrices. For example, |0>⊗|0> + |1>⊗|1> is entangled and has tensor products. I think that Xcelerate is correct in saying that all combinations of the basis vectors form the basis of the multi-particle Hilbert space, as a single-particle wavefunction is just a vector/ket.
- monktastic1 10y agoSure, the tensor product space has a basis that is formed by the tensor products of all pairs of basis elements. But this is different from saying that any particular vector in the space is a tensor product of elements from the individual spaces. But I'm possibly just misunderstanding what you're saying.
- deleted 10y ago[deleted]
- codethief 10y agoFair enough, I should have been more precise: By "all possible tensor products" I actually meant all elements in the tensor product space, including all linear combinations of tensor products of single-particle states.
- HeavenBanned 10y agothis comment chain is getting legendary rn ...best of HN for real. i'm wondering what max tegmark was saying about computers simulating the MWI and physicists confirming/nonconfirming MWI via computational simulation.