Computational Chemistry

4.2 The Development of Quantum Mechanics.

The Schr€odinger Equation

4.2.1 The Origins of Quantum Theory: Blackbody Radiation

and the Photoelectric Effect

Three discoveries mark the transition from classical to modern physics: quantum
theory, radioactivity, and relativity (Fig.4.1). Quantum theory had its origin in the
study of blackbody radiation and the photoelectric effect.

4.2.1.1 Blackbody Radiation

A blackbody is one that is a perfect absorber of radiation: it absorbs all the radiation
falling on it, without reflecting any. More relevant for us, the radiation emitted by a
hot blackbody depends (as far as the distribution of energy with wavelength goes)
only on the temperature, not on the material the body is made of, and is thus
amenable to relatively simple analysis. The sun is approximately a blackbody; in
the lab a good source of blackbody radiation is a furnace with blackened insides and
a small aperture for the radiation to escape. In the second half of the nineteenth
century the distribution of energy with respect to wavelength that characterizes
blackbody radiation was studied, in research that is associated mainly with Lummer
and Pringsheim [ 1 ]. They plotted the fluxDF(in modern SI units, J s"^1 m"^2 ) per
wavelength emitted by a blackbody over a wavelength rangeDlversus the wave-
length, for various temperatures (Fig.4.2):DF/Dlversusl. The result is a histo-
gram or bar graph in which the area of each rectangle is (DF/Dl)Dl¼DFand
represents the flux (energy per second per unit area) emitted in the wavelength
range covered by thatDl;DF/Dlcan be called the flux density for that particular

classical physics (physics before 1900)

mechanics

Galileo, Newton, etc.

optics

Newton, Huygens, Young

electromagnetism

Faraday, Maxwell

modern physics (after 1900)

quantum theory

Planck, Einstein, etc.

radioactivity

Becquerel

relativity

Einstein

blackbody

radiation photoelectric

effect

Fig. 4.1 The discoveries marking the transition from classical to modern to physics. Although
radioactivity was discovered in 1896, its understanding had to wait for relativity and quantum
theory

4.2 The Development of Quantum Mechanics. The Schr€odinger Equation 87