Page 106 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch08 Elementary Physical Chemistry

Introduction to Quantum Theory 91

went back to the Bohr theory of the hydrogen atom. The phenomenal
success of Bohr’s theory of the hydrogen atom could not be entirely
accidental, he reasoned. There must be some essential validity to that
approach. In Bohr’ theory, there are concepts that can be measured
and concepts that cannot be measured. Heisenberg decided to develop
a theory based solely on concepts that have been measured. The Bohr
theory uses such quantities as energy levels, frequencies, intensities and
orbits. Heisenberg argued that all we know for sure about the atom are
such things as frequencies, intensities of the emitted light. No one has
seen orbits — out they go. In fact, no one has seen energy levels, only
changes in energy levels.
Heisenberg found that he could obtain the correct results for the
harmonic oscillator and the hydrogen atom by replacing the classical
dynamical variables, which depend on single numbers, by matrices
which are arrays of numbers. He even worked out the mathematics on
how to handle multiplication of arrays of numbers, not knowing that
mathematicians had done that ∼100 years earlier under the name of
matrix multiplication.
When Heisenberg returned to Gottingen, he showed his work to Born,
who immediately recognized that Heisenberg’s work was not a mere
mathematical scheme for handling arrays of numbers (which was not
new), but what Heisenberg actually had developed laid the foundation
of a new and different theoretical framework of mechanics.
Together with Jordan, a young faculty member at Gottingen,
Heisenberg, Born and Jordan formulated a general theory of quantum
mechanics which, because of the form, is also referred to as matrix
mechanics.
(3) By now Dirac came on the scene. Heisenberg, on a visit to Cambridge
University, showed his work to Prof. Fowler, asking him for his opinion.
Fowler gave the material to Dirac, a student of Fowler, and asked him
for comments. Dirac not only did that, but formulated a quantum
theory in terms of operators.
Dirac’s formulation is lean in comparison with Heisenberg’s, accom-
plishing with ease what Heisenberg, Born and Jordan could accomplish
only with great difficulty. Dirac’s formulation is most elucidating
in its generality and is sometimes referred to as symbolic quantum
mechanics.