15 votes

On the nature of zero-point energy (ZPE)

In the Born-Oppenheimer approximation nuclei are assumed to behave as classical point-like particles. However, in reality the wave-particle duality also applies to them, and so the Schrödinger ...
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10 votes

Quantum harmonic oscillator, zero-point energy, and the quantum number n

The zero-point energy is of no importance here, since you can always choose your reference energy freely you can energy-shift your hamiltonian by $\frac{1}{2}\hbar\omega$ $$ H = \frac{p^2}{2m}+\frac{1}...
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7 votes

VASP output energy

Always use the energy after extrapolation back to 0 K. The energy before the extrapolation is just from your smearing method and is a fictitious value.
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6 votes

Quantum harmonic oscillator, zero-point energy, and the quantum number n

The quantum number n simply represents the different energy levels given by the harmonic oscillator. $\mathbf{n=0}$ does not correspond to a given temperature, but its relative occupation to other ...
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5 votes

Quantum harmonic oscillator, zero-point energy, and the quantum number n

As has been stated in several other answers already, $n$ is only a number, and the population of the states with different $n$ depends on the temperature. However, an important point has not yet been ...
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5 votes

Quantum harmonic oscillator, zero-point energy, and the quantum number n

Is $𝑛$ only a number? In short, $n$ is the energy quantum number of the quantum harmonic oscillator. If so then how does $𝑛$=$0$ have anything to do with temperature? In particular, $n$=$0$ means ...
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5 votes

Quantum harmonic oscillator, zero-point energy, and the quantum number n

Is $n$ only a number? $n$ is indeed a number. Is it only a number? Well it's a quantum number which means it labels the $n^{\textrm{th}}$ excited energy level of the system (i.e. the $(n+1)^{\textrm{...
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3 votes

On the nature of zero-point energy (ZPE)

The Born-Oppenheimer (BO) approximation works well at high temperatures (far from 0 K), but the quantum nature of the nuclei (i.e. the zero-point energy) is an important consideration at low ...
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