- ... nuclei2.1
- At the
atomic energy scales which are of interest in this work, the nuclei are
extremely well-described as massive point charges and their
internal structure is
safely neglected.
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- ... particle2.2
- We are neglecting spin in this
discussion.
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- ... eigenvalue2.3
- For the case of eigenvalue degeneracy, the state-vector collapses to a vector lying in the subspace spanned by all of the eigenvectors corresponding to the measured eigenvalue.
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- ... measurement2.4
- Again, for the degenerate case, the probabilities must be summed for all eigenvectors corresponding to the measured eigenvalue.
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- ... operators2.5
- For a linear operator ,
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- ...
equation2.6
- Atomic units are used throughout (unless otherwise stated):
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- ... problem2.7
- The most notable exception to this rule is the motion of hydrogen, which is often treated using the path-integral formulation of quantum mechanics[9,10].
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- ... express2.8
- Berry [13] has recently proposed a non-relativistic explanation involving a geometric phase.
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- ...
operators2.9
- Neither the creation nor annihilation
operators are Hermitian, and so they do not correspond to physical observables.
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- ... states3.1
- Our restriction to non-spin-polarised
systems requires that be even.
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- ... potential3.2
- The chemical hardness has been proposed as a quantity which gives a more reliable indication of pseudopotential transferability since it includes self-consistent effects [63,64].
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- ... density-matrix4.1
- The computational cost of diagonalising a sparse density-matrix scales as the square of the system-size.
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- ... reciprocal-space7.1
- The conventions used here for
discrete Fourier transforms are
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