important, the other forms are more appropriate to use. We will find later that
for atomic and molecular systems, the Hamiltonian function is used almost
exclusively.
Before we leave this topic, it is important to recognize what these equations
of motion provided. If one could indeed specify the forces acting on a parti-
cle, or a group of particles, one could predict how those particles would be-
have. Or if one knows the exact form of the potential energy of the particles
in the system, or if one wants to know what the total energy of the system is,
one could still model the system. Nineteenth-century scientists were compla-
cent in their feeling that if the proper mathematical expressions for the poten-
tial energy or forces were known, then the complete mechanical behavior of
the system could be predicted. Newton’s, Lagrange’s, and Hamilton’s equations
endowed scientists with a feeling of certainty that they knew what was going
on in the world.
But with what type of systems were they dealing? Macroscopic ones, like a
brick, a metal ball, a piece of wood. Since Dalton had enunciated his version
of the modern atomic theory, the objects of matter called atoms must follow
the same equations of motion. After all, what were atoms but tiny, indivisible
pieces of matter? Atoms should behave no differently than regular matter does
and would certainly be expected to follow the same rules. However, even as the
Hamiltonian function was introduced as a new way to describe the motion of
matter, some scientists started looking a little more closely at matter. They
could not explain what they saw.9.3 Unexplainable Phenomena
As science developed and advanced, scientists began to study the universe
around them in different and new ways. In several important instances, they
were not able to explain what they observed using contemporary ideas. It
seems easy in hindsight to suggest that new ideas would be necessary. However,
at that point no phenomena had been observed that would not be understood
using the known science of the time. One must also understand the nature of
the people who did the work: educated in the shadow of an assumed under-
standing of nature, they expectedthat nature would follow these rules. When
unusual experimental results were measured, explanations were attempted
based on classical science. It soon became clear that classical science could not
explain certain observations, and cannot even to this day. It remained the task
of a new generation of scientists to understand and explain the phenomena
(with several important exceptions, almost everyone involved in the develop-
ment of quantum mechanics was relatively young).
The unexplained phenomena were the observation of atomic line spectra,
the nuclear structure of the atom, the nature of light, and the photoelectric ef-
fect. Certain experimental observations in these areas did not conform to the
expectations of classical mechanics. But to really see why a new mechanics was
necessary, it is important to review each of these phenomena and understand
why classical mechanics did not explain the observations.9.4 Atomic Spectra
In 1860, the German chemist Robert Wilhelm Bunsen (of Bunsen burner
fame) and the German physicist Gustav Robert Kirchhoff invented the spec-
troscope. This apparatus (Figure 9.4) used a prism to separate white light into248 CHAPTER 9 Pre-Quantum Mechanics