that fit the facts, and then tried to interpret the equation theoretically. To do this he
had to make two assumptions:
- The total energy possessed by the oscillators in the frequency rangenþdn(nis
the Greek letternu, commonly used for frequency, not to be confused withv,
vee, commonly used for velocity) is proportional to the frequency:
EtotðnþdnÞ/n (4.1)- The emission or absorption of radiation of frequencynby the collection of
oscillators is caused by jumps between energy levels, with loss or gain of a
quantity of energykn:
DE¼kn (4.2)The constantk, now recognized as a fundamental constant of nature, 6.626&
10 "^34 J s particle"^1 , is called Planck’s constant, and is denoted byh, so Eq.4.2
becomes
DE¼hn '(4:3)Why the letterh? Evidently becausehis sometimes used in mathematics to
denote infinitesimals and Planck intended to let this quantity go to zero (this was
suggested to me by the late Professor Philip Morrison of MIT). In the event, it
turned out to be small but finite. Apparently the letter was first used to denote the
new constant in a talk given by Planck at a meeting (Sitzung) of the German
Physical Society in Berlin, on 14 December 1900 [ 4 ]. The interpretation of
Eq.4.3, a fundamental equation of quantum theory, as meaning that the energy
represented by radiation of frequencynis absorbed and emitted in quantized
amountshn(definite, constrained amounts; jerkily rather than continuously) was,
ironically, apparently never fully accepted by Planck [ 5 ]. Planck’s constant is a
measure of the graininess of our universe: because it is so small processes
involving energy changes often seem to take place smoothly, but on an ultrami-
croscopic scale the graininess is there [ 6 ]. The constanthis the hallmark of
quantum expressions, and its finite value distinguishes our universe from a
nonquantum one.
4.2.1.2 The Photoelectric Effect
An apparently quite separate (but in science no two phenomena are really ever
unrelated) phenomenon that led to Eq.4.3, which is to say to quantum theory, is the
photoelectric effect: the ejection of electrons from a metal surface exposed to light.
4.2 The Development of Quantum Mechanics. The Schr€odinger Equation 89