Black-body radiation experiment Updated 2025-07-16
- The Quantum Story by Jim Baggott (2011) page 10 mentions:and the footnote comments:
Early examples of such cavities included rather expensive closed cylinders made from porcelain and platinum.
- 1859-60 Gustav Kirchhoff demonstrated that the ratio of emitted to absorbed energy depends only on the frequency of the radiation and the temperature inside the cavity
- 1896 Wien approximation seems to explain existing curves well
- 1900 expriments by Otto Lummer and Ernst Pringsheim show Wien approximation is bad for lower frequencies
- 1900-10-07 Heinrich Rubens visits Planck in Planck's villa in the Berlin suburb of Grünewald and informs him about new experimental he and Ferdinand Kurlbaum obtained, still showing that Wien approximation is bad
- 1900 Planck's law matches Lummer and Pringsheim's experiments well. Planck forced to make the "desperate" postulate that energy is exchanged in quantized lumps. Not clear that light itself is quantized however, he thinks it might be something to do with allowed vibration modes of the atoms of the cavity rather.
- 1900 Rayleigh-Jeans law derived from classical first principles matches Planck's law for low frequencies, but diverges at higher frequencies.
Black-body Radiation Experiment by sciencesolution (2008)
Source. A modern version of the experiment with a PASCO scientific EX-9920 setup. Bohr model Updated 2025-07-16
Was the first model to explain the Balmer series, notably linking atomic spectra to the Planck constant and therefore to other initial quantum mechanical observations.
This was one of the first major models that just said:
I give up, I can't tie this to classical physics in any way, let's just roll with it, OK?
It still treats electrons as little points spinning around the nucleus, but it makes the non-classical postulate that only certain angular momentums (and therefore energies) are allowed.
Bibliography:
- Inward Bound by Abraham Pais (1988) Chapter 9.e Atomic structure and spectral lines - Niels Bohr
- The Quantum Story by Jim Baggott (2011) Chapter 3 A Little Bit of Reality
Causality and quantum jumps are incompatible Updated 2025-07-16
If something does a quantum jump, what causes it to decide doing so at a particular time and not another? It is expected that a continuous cause would have continuous effects.
This concern was raised immediately by Rutherford while reviewing the Bohr model in 1913 as mentioned in The Quantum Story by Jim Baggott (2011) page 32.
Corpuscular theory of light Updated 2025-07-16
The Quantum Story by Jim Baggott (2011) page 2 mentions how newton's support for the corpuscular theory of light led it to be held for a very long time, even when evidence of the wave theory of light was becoming overwhelming.
Planck's law Updated 2025-07-16
Used to explain the black-body radiation experiment.
Published as: On the Theory of the Energy Distribution Law of the Normal Spectrum by Max Planck (1900).
The Quantum Story by Jim Baggott (2011) page 9 mentions that Planck apparently immediately recognized that Planck constant was a new fundamental physical constant, and could have potential applications in the definition of the system of units (TODO where was that published):This was a visionary insight, and was finally realized in the 2019 redefinition of the SI base units.
Planck wrote that the constants offered: 'the possibility of establishing units of length, mass, time and temperature which are independent of specific bodies or materials and which necessarily maintain their meaning for all time and for all civilizations, even those which are extraterrestrial and nonhuman, constants which therefore can be called "fundamental physical units of measurement".'
TODO how can it be derived from theoretical principles alone? There is one derivation at; en.wikipedia.org/wiki/Planck%27s_law#Derivation but it does not seem to mention the Schrödinger equation at all.
Quantum number Updated 2025-07-16
Quantum numbers appear directly in the Schrödinger equation solution for the hydrogen atom.
However, it very cool that they are actually discovered before the Schrödinger equation, and are present in the Bohr model (principal quantum number) and the Bohr-Sommerfeld model (azimuthal quantum number and magnetic quantum number) of the atom. This must be because they observed direct effects of those numbers in some experiments. TODO which experiments.
E.g. The Quantum Story by Jim Baggott (2011) page 34 mentions:This refers to forbidden mechanism. TODO concrete example, ideally the first one to be noticed. How can you notice this if the energy depends only on the principal quantum number?
As the various lines in the spectrum were identified with different quantum jumps between different orbits, it was soon discovered that not all the possible jumps were appearing. Some lines were missing. For some reason certain jumps were forbidden. An elaborate scheme of ‘selection rules’ was established by Bohr and Sommerfeld to account for those jumps that were allowed and those that were forbidden.
Quantum Numbers, Atomic Orbitals, and Electron configurations by Professor Dave Explains (2015)
Source. He does not say the key words "Eigenvalues of the Schrödinger equation" (Which solve it), but the summary of results is good enough.