A universal constant of the utmost importance in the formulation of the laws on nature known as

quantum mechanics. Planck’s Constant is represented by the letter

h, and has units of

energy times

time.

h = 6.626 x 10^{-34} J-s or 4.136 x 10^{-15} ev-s

In a way, h *is* quantum mechanics, because it relates the discrete phenomena of the quantum realm to the observable properties of macroscopic realm. The need for such a constant of proportionality, and therefore a quantum view of nature, first arose because of the well known results of two oft-repeated experiments around the turn of the 20th century. One was the ‘photoelectric effect,’ in which metal objects were shown to emit electrons when bombarded with electromagnetic radiation. In light of what classical electrodynamics and mechanics had to say about electromagnetic waves, incoming radiation at any frequency should cause the emission, provided it was at a high enough intensity. However, the experiments showed that there was a ‘cutoff frequency’ below which no electrons were emitted no matter what the intensity. It seemed that the emission was not a cumulative effect of the total power delivered to the metal but a result of what energy was being delivered instantaneously.

The other experimental result was the ‘blackbody radiation’ phenomenon. It was observed that an insulated heated chamber, a so-called ‘*blackbody,*’ emitted a spectrum of radiation through a tiny opening that was proportional to the temperature of the chamber in a way that was not consistent with the known laws of classical electrodynamics. Classical electrodynamics predicted much more radiation at short frequencies than was observed. This discrepancy troubled physicists at the turn of the century so much that it was known as the ‘*Ultraviolet Catastrophe*.’ Through a complicated analysis of the resonant ‘modes’ of waves in such a cavity, it was shown in 1900 by the German physicist Max Planck that the observed spectrum could be explained if the light could be available in discrete quanta which themselves were proportional to the frequency in the following way:

E = hν

Where E is the energy, ν is the frequency of the radiation, and h is the constant of proportionality in question, which was named for Planck. This same result could obviously explain the photoelectric effect, and in 1905 Albert Einstein proposed just that.

In the following two decades, this constant of proportionality was used to explain quantum phenomena of matter. First h made its way into Niels Bohr’s ultimately incomplete early quantum theory, when he proposed that the electron of a hydrogen atom could only occupy discrete states in which the angular momentum was a multiple of h. It was later proposed by Louis de Broglie in 1921 that matter had an associated wavelength, and it was proportional to h:

λ = h / p

This led directly to the development in the next few years of our complete quantum theory of matter, quantum mechanics. h appears in the Shrodinger Equation of non-relativistic quantum mechanics, and the Dirac Equation of relativistic quantum mechanics. In quantum mechanical analysis, it turns out that the quantity most often used is h/2π, and this is given the special symbol h(bar).