This
is a theory based on using the concept of the quantum unit to describe
the dynamic properties of matter and radiation. The foundation was laid
by the German physicist Max Planck, who discovered in 1900 that energy
can be emitted or absorbed by matter only in small, definite units called
quanta. An exciting section of this theory is the uncertainty principle,
discovered by the German physicist Werner Heisenberg in 1927, which states
that the position and speed of a particle cannot be specified at the same
time.

# Early History

In the
18th and 19th centuries, Newtonian, or classical, mechanics appeared to
provide a wholly accurate description of the motions of bodies—for example,
planetary motion. In the late 19th and early 20th centuries, however, many
discoveries began to doubt Newton. One of them were the lines that appear
in the spectra of light emitted by heated gases, or gases in which electric
discharges take place. From the model of the atom developed in the early
20th century, scientists had also expected that the electrons would emit
light over a broad frequency (no. of waves per second) range, rather than
in the narrow frequency ranges that form the lines in a spectrum.

Another
puzzle for physicists was the coexistence of two theories of light: the
corpuscular theory, which explains light as a stream of particles, and
the wave theory, which views light as electromagnetic waves. A third problem
was the absence of a molecular basis for thermodynamics. In his book *Elementary
Principles in Statistical Mechanics* (1902), the American physicist
J. Willard Gibbs believed that it was impossible to discover a theory which
could explain molecular action, thermodynamics, radiation, and electrical
phenomena as they were then understood.

# Planck's Introduction of the
Quantum

At the
turn of the century, physicists did not yet clearly recognize that these
and other difficulties in physics were in any way related. The first development
that led to the solution of these difficulties was Planck's introduction
of the concept of the quantum, as a result of physicists' studies of blackbody
radiation. (The term *blackbody* refers to an ideal body or surface
that absorbs all light without any reflection.) A body at a high temperature—a
“red heat”—gives off most of its radiation in the low frequency (red and
infrared) regions; a body at a higher temperature—“white heat”—gives off
more radiation in higher frequencies (yellow, green, or blue). During the
1890s physicists studied these phenomena and expressed their results in
a series of curves or graphs. The classical theory predicted an altogether
different set of curves from those actually observed. What Planck did was
to devise a mathematical formula that described the curves exactly; he
then deduced a physical hypothesis that could explain the formula. His
hypothesis was that energy is radiated only in quanta of energy *h*u,
where u is the frequency and *h* is the quantum action, now known
as Planck's constant.

# Einstein's Contribution

The next
important developments in quantum mechanics were the work of German-born
American physicist and Nobel laureate Albert Einstein. He used Planck's
concept of the quantum to explain the photoelectric effect—a phenomenon
in which electrons are emitted from metal surfaces when light falls on
these surfaces.

According
to classical theory, the energy, as measured by the voltage of the emitted
electrons, should be proportional to the intensity (concentration) of the
radiation. The energy of the electrons, however, was found to be independent
of the intensity of radiation—which determined only the number of electrons
emitted—and to depend solely on the frequency of the radiation. The higher
the frequency of the incident ("falling") light waves, the greater is the
electron energy; below a certain frequency no electrons are emitted. These
facts were explained by Einstein by assuming that a single quantum of radiant
energy ejects a single electron from the metal. The energy of the quantum
is proportional to the frequency, and so the energy of the electron depends
on the frequency.

# The Bohr Atom

In 1911
Rutherford discovered the atomic nucleus. He assumed, on the basis of experimental
evidence, that every atom consists of a dense, positively charged nucleus,
surrounded by negatively charged electrons revolving around the nucleus
as planets revolve around the sun. The classical electromagnetic theory
developed by the British physicist James Clerk Maxwell predicted that an
electron revolving around a nucleus will continuously produce light energy
until it has lost all its energy, and eventually will fall into the nucleus.
Thus, according to classical theory, an atom, as described by Rutherford,
can't exist for a long time. This led the Danish physicist Niels Bohr,
in 1913, to suggest that in an atom the classical theory does not hold,
and that electrons move in fixed orbits. Every change in orbit by the electron
corresponds to the absorption or emission of a quantum of radiation.

It was
difficult to prove Bohr's theory to atoms with more than one electron.
The mathematical equations for the next simplest atom, the helium atom,
were solved during the 1910s and 1920s, but the results were not entirely
proved by experiment. For more complex atoms, only approximate solutions
of the equations are possible, and these don't agree with observations.

# Wave Mechanics

The French
physicist Louis Victor de Broglie suggested in 1924 that because electromagnetic
(light, x-ray, infra-red, etc.) waves can behave like particles, particles
should, in some cases, also behave like wave. This prediction was proved
within a few years by the American physicists Clinton Joseph Davisson and
Lester Halbert Germer and the British physicist George Paget Thomson. They
showed that a beam of electrons scattered by a crystal produces a pattern characteristic of a wave. The wave concept of a particle led the
Austrian physicist Erwin Schrödinger to develop a so-called wave equation
to describe the wave properties of a particle.

Although
this equation was gave solutions for all points in space, the solutions
of the equation could only work in certain conditions called eigenfunctions
(German *eigen,* “own”). The Schrodinger wave equation thus had only
certain solutions; these solutions were mathematical expressions in which
quantum numbers appeared as parameters. (Quantum numbers are integers developed
in particle physics to give the size of certain quantities of particles
or systems.) The Schrodinger equation was solved for the hydrogen atom
and gave conclusions which agreed with earlier quantum theory. Moreover,
it was solvable for the helium atom, which earlier theory had failed to
explain, and here also it was in agreement with experiments. The solutions
of the Schrodinger equation also indicated that no two electrons could
have exactly the same amount of energy. This rule is called the exclusion
principle.

# The Meaning of Quantum Mechanics

Even
for the simple hydrogen atom, which consists of two particles, mathematical
results are extremely complex. The next simplest atom, helium, has three
particles, and even in the simple mathematics of classical dynamics, the
three-body problem is not entirely soluble. The energy levels can be calculated
accurately, however, even if not exactly. In applying quantum mathematics
to complex situations, a physicist can use one of a number of mathematical
formulas. The choice depends on the suitable approximate solutions.

Although
quantum mechanics describes the atom purely mathematically, a rough description
can be given of what the atom is now thought to be like. Surrounding the
nucleus is a series of stationary waves; these waves have crests at certain
points, each complete standing wave representing an orbit. The absolute
square of the amplitude of the wave at any point is a measure of the probability
that an electron will be found at that point at any given time. Thus, an
electron can no longer be said to be at any precise point at any given
time.

**The Uncertainty Principle
**

Heisenberg,
in 1927 formulated the uncertainty principle. This principle states that
it is impossible to calculate the position and speed of a particle at the
same time. In other words, the more accurately a particle's speed is measured
and known, the less accuracte the position can be measured. This principle
is also fundamental to the understanding of quantum mechanics as it is
generally accepted today: The wave and particle character of electromagnetic
radiation can be understood as two complementary properties of radiation.