book_cover_big.gifWhile the quantum mechanical framework was being developed after Plank’s discovery in 1901, physicists were wrestling with the dual character of light (wave or particle?). Thomas Young’s double slit experiment in 1803, where interference patterns were observed, seemed to show without doubt that light was a wave phenomenon. However, Planck’s interpretation of black body radiation as light quanta, followed by Einstein’s explanation of the photoelectronic effect, both contradicted the light-as-wave theory. Additionally, a shocking discovery was made by Compton in 1925. Compton found that when he let X-rays (a form of light with extremely short wavelengths) collide head-on with a bundle of electrons, the X-rays were scattered as if they were particles. This phenomenon became known as the “Compton scattering experiment.”

At about that time, French physicist Louis de Broglie combined two simple formulas: Plank’s light quanta expression (E = hν, with ν as the frequency) and Einstein’s famous energy‑mass equation (E = mc2). This led to another simple equation: λ = h/mc, with λ as wavelength. This equation really tells us that all matter has wave properties. However, since the mass, m, of most everyday visible objects is so large, their wavelengths are too small for us to notice any wave effect. But when we consider the small masses of atomic particles such as electrons and protons, their wavelengths become relevant and start to play a role in the phenomena we observe.

All this brought Erwin Schrödinger to the conclusion that electrons should be considered waves, and he developed a famous wave equation that very successfully described the behavior of electrons in a hydrogen atom. Schrödinger’s equation used a wave function to describe the probability of finding a rapidly moving electron at a certain time and place. In fact, the equation confirmed many ideas that Bohr used to build his empirical atom model. For instance, the equation correctly predicted that the lowest energy level of an atom could allow only two electrons, while the next level was limited to eight electrons, and so on. In the year 1933 Schrödinger was awarded the Nobel Prize for his wave equation.

Schrödinger had, as did Planck and Einstein, an extensive background in thermodynamics. From 1906 to 1910, he studied at the University of Vienna under Boltzmann’s successor, Fritz Hasenöhrl. Hasenöhrl was a great admirer of Boltzmann and in 1909 he republished 139 of the latter’s scientific articles in three volumes [Hasenöhrl, 1909]. It was through Hasenöhrl that Schödinger became very interested in Boltzmann’s statistical mechanics. He was even led to write of Boltzmann, “His line of thoughts may be called my first love in science. No other has ever thus enraptured me or will ever do so again [Schrödinger 1929].Later he published books, (Statistical Thermodynamics and What’s Life), and several papers on specific heats of solids and other thermodynamic issues. [1]

 © 2009 Copyright John Schmitz

[1] Taken from “The Second Law of Life”:


book_cover_big.gifAround 1900, Planck was an expert in classical thermodynamics and wrote many articles and books about that theory. The concept of entropy especially held his interest, but he published also in the fields of dilute solutions and thermoelectricity. Of course, being a time-oriented fellow, he was familiar with the results of Boltzmann’s works. However, being a physicist of the “old school,” he was raised without having the concept of atoms in his scientific toolkit. In 1891, for instance, he and Ostwald had a discussion with Boltzmann at a conference where Planck stated that thermodynamic methods without the incorporation of atomistic models were sufficient to explain those days’ physical observations. Also, Planck was not very pleased with the statistical approach of Boltzmann [1]. His main objection was that Boltzmann’s statistical approach allowed that the change of entropy for spontaneous processes could become negative (i.e., an entropy decrease), although at an extremely low probability (see Chapter 3 for more details on this topic).

But Planck was wrestling at the turn of the century with understanding black body radiation behavior. Since 1861, when Kirchhoff[2] first described a black body, the radiation behavior was studied and described by a slew of well-known physicists such as Wien, Stefan, and Boltzmann. However, all these attempts led only to a radiation law that had very limited applicability. The breakthrough in Planck’s understanding came when he started to use Boltzmann’s statistical approach. In fact, it was Planck who wrote the current well-known form of the Boltzmann equation, S = k lnW, in his famous 1901 article[3] . It was in this text that Planck proposed that the radiation might consist of small packets (quanten) of size hv. This was the beginning of quantum mechanical theory. Planck struggled a long time with his own thoughts, since they were so in contrast with the classical belief of continuous energy. For some time he saw his quanten approach merely as a mathematical trick, but slowly became convinced that energy in nature was indeed discrete, rather than a continuum. It also took some time before his ideas were accepted in the scientific community[4]. It was no less than Einstein who used the quanta principle to explain the photoelectronic effect, as we will see shortly.

[1] Flamm, Dieter, “Einführung zu Ludwig Boltzmanns Entropy und Wahrscheinlichkeit”, this is an introduction of Entropie und Warscheinlichkeit, 1872-1905 von Ludwig Boltzman in Ostwalds Klassiker der Exakten Wissenschaften, Band 286, Verlag Harri Deutsch, Frankfurt am Main (2000). This book is contains a nice compilation of the most important articles from Boltzmann in original version.

[2] It’s likely that Planck got his interest in black body radiation from Kirchhoff, who was his teacher. In 1889, he succeeded Kirchhoff as professor at the University of Berlin.

[3] Planck, Annalen der Physik 1901

[4] Interestingly, Planck once remarked that a new theory gets accepted not because its opponents become convinced, but because they eventually die and new generations of scientists, unhindered by historic baggage, simply assume the theory is true (provided that it is still supported by experimental facts)!

© Copyright 2009 John Schmitz