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In earlier DFT studies of ferroelectric materials, GGAs such as PBE were avoided as they tended to exaggerate the ferroelectric distortion. Instead, LDA calculations were performed and an artificial negative pressure was applied to compensate for LDA otherwise overestimating lattice constants Philippe Ghosez, Javier Junquera: cond-mat/0605299 "First-...

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How can I do this, which tests would you recommend me to perform on my grid? When developing new code, the standard thing to do to ensure your code works as expected is to compare it to known solutions. For some mathematical models, there are closed form expressions (i.e., analytic solutions) and you can use these as a basis for testing. For instance, ...

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Why are numerical solutions necessary in order to plot this? They aren't. Numerical solutions of the TDSE are only necessary when no analytical solution is known. The only real-world reason for implementing a numerical solution of the Schrödinger equation when there are analytical solutions available that makes sense is when you're implementing a multi-...

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From a theoretical point of view, a quantum mechanical system consists of a Hilbert space $\mathcal H$, which consists (roughly) of the possible states of the system, and a special choice of operator which governs how the system evolves in time. When we make a choice for this time evolution operator, we call it the Hamiltonian. A quantum mechanical ...

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