A 1929 paper by Felix Bloch, Über die Quantenmechanik der Elektronen in Kristallgittern, is widely cited as having predicted the phenomenon of Bloch oscillations: The oscillatory motion of an electron in a periodic potential when a constant force is applied.

Is this attribution correct?

The 1929 paper has a section (starting on page 572) where the effect of a uniform electric field on the electrons in a crystal is considered, but I could not find any mention of oscillatory motion in that section or elsewhere in the paper. Did I overlook something?

The first explicit mention of periodic motion that I am aware of is in a 1934 paper by Clarence Zener, A theory of the electrical breakdown of solid dielectrics:

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Perhaps we should speak of "Zener oscillations" ? I note that the term "Bloch-Zener oscillations" is used in the literature, but that refers to the superposition of Bloch oscillations and Zener tunnelling, not to the oscillations per se.

I reproduce here the translation the paragraphs in Bloch's 1929 paper that adress the motion of the electrion in a uniform magnetic field (page 572). No mention is made of the oscillatory motion that follows from equation 48.

$$\frac{d}{dt}|c_{klm}|^2=-\frac{KeF}{h}\frac{\partial}{\partial k}|c_{klm}(0)|^{2},\;^{\ast}\qquad\qquad(48)$$

It can be seen that if initially the amplitudes of the eigenfunctions building up our wavepacket are given by (46), this distribution of the amplitudes in the $k,l,m$-space shifts towards increasing values of $k$, more rapidly the larger the field strength $F$ is. In the limit of perfectly free electrons, (48) passes directly into that, what one would expect according to classical mechanics. According to (9) then the velocity in the $x$-direction is given by


and instead of (48) one can write

$$\frac{d}{dt}|c_{klm}|^2=-\frac{eF}{m}\frac{\partial}{\partial v_x}|c_{klm}|^2.$$

This would also be expected classically, when a cloud of electrons experiences an acceleration $\frac{eF}{m}$.$^{\ast\ast}$

$^\ast$ Mr. Peierls has kindly pointed out to me that one can derive equation (48) also independently of the special form (41) of the wave packet. It does seem in any case necessary that the initial stationary state is not sharply defined.
$^{\ast\ast}$ Cf. E.H. Kennard, l.c.

  • 3
    $\begingroup$ Isn't this the typical theme of Stigler's law of eponymy? A large number of named effects are not named after the right person. $\endgroup$
    – AChem
    May 11 at 14:16
  • $\begingroup$ Given the original German paper of Felix Bloch pwein.at/physics/Lectures/Famous-Papers/… does anyone have or know of an English translation of it? There exists a partial translation courses.physics.ucsd.edu/2018/Fall/physics211a/topic/bloch.pdf, though it is nothing compared to the 46 pages original paper. $\endgroup$
    – Sha
    May 13 at 2:32
  • $\begingroup$ @Sha --- I don't know of an english translation of the entire paper, but I have translated the text that addresses the motion in a uniform electric field. There Bloch could very well have noted the oscillatory motion, but he does not. $\endgroup$ May 13 at 6:17
  • $\begingroup$ @CarloBeenakker Thanks. I think reading and analyzing the entire paper would be the best way to reach a definitive conclusion. Unfortunately, I do not know German language. By the way, I think translating and maybe commenting on this paper would be a great research task. I hope to see this accomplished someday. $\endgroup$
    – Sha
    May 13 at 7:03


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