What is Harmonic oscillator, force constant, reduced mass, zero-point energy?

Example 1.6 (The canonical commutator)

For any function $f$, $\hat x\hat pf = -\iu\hbar xf'$ and $\hat p\hat xf = -\iu\hbar(f + xf')$. The difference is $[\hat x,\hat p]f = \iu\hbar f$, so $[\hat x,\hat p] = \iu\hbar$: position and momentum do not commute. This single relation underlies the uncertainty principle and, below, the whole spectrum of the harmonic oscillator.

Example 1.22 (Zero-point energies of $\ce{H2}$ and $\ce{D2}$)

The harmonic wavenumbers are $\tilde\omega_e = 4401.2\,\mathrm{cm}^{-1}$ for $\ce{H2}$ and $3115.5\,\mathrm{cm}^{-1}$ for $\ce{D2}$, in the ratio $1.413$, close to $\sqrt2$: same bond and force constant, doubled reduced mass. The harmonic zero-point energies are half these, 2200.6 and $1557.8\,\mathrm{cm}^{-1}$, $26.3\,\mathrm{kJ}/\mathrm{mol}$ and $18.6\,\mathrm{kJ}/\mathrm{mol}$. A molecule can never lose this energy; the difference between isotopes is the source of the isotope effects of Chapters 11 and 12.

Example 1.29 (The ionisation energy of hydrogen)

$hcR_\infty = 13.6057\,\mathrm{eV}$ and $\mu/m_e = 1/(1 + m_e/m_p) = 0.999456$, so $-E_1 = 13.598\,\mathrm{eV}$: the measured ionisation energy of hydrogen, to the last digit given in the Year 1 volume. The reduced mass changes the fourth significant figure.