194 The Poetry of Physics and The Physics of Poetry
a point particle. Max Born was the first to make the probabilistic
interpretation of Schrödinger’s results. He was most likely influenced by
the 1924 work of Bohr, Kramer and Slater in which they claimed that the
electromagnetic wave represented the probability of detecting a photon.
Schrödinger resisted the probabilistic interpretation at first because
he felt that he had eliminated the discontinuity of quantum jumps by
considering the electron as a material wave. After Bohr had finally
convinced him that his theory was correct but his interpretation not valid,
Schrödinger remarked in frustration, “If one has to stick to this quantum
jumping, then I regret ever having gotten involved in this thing”.
Six months prior to Schrödinger’s developments in the summer
of 1925 Heisenberg independently developed a completely different
approach to atomic theory. His mathematical description of the atom
known as matrix mechanics also dealt with probabilities. Heisenberg
argued that atomic theory should only deal with observable i.e.
quantities that can be directly measured. He, therefore, developed
equations for the probabilities that an atom would make a transition form
one quantum state to another. Heisenberg formulated his equation in the
quantum domain for which Bohr’s correspondence principle was valid.
This enabled him to exploit classical physics, which is still valid in this
domain. Using his equations, Heisenberg was able to calculate correctly
the probabilities of transitions from one atomic level to another, as well
as the energies of each level.
Schrödinger was able to show that his wave mechanics and
Heisenberg’s matrix mechanics were mathematically identical.
Schrödinger’s formulation of quantum mechanics proved to be more
convenient for actual calculations. Heisenberg’s contribution was just as
important, however. Although calculations within Heisenberg’s matrix
mechanics were clumsier, his scheme proved extremely useful from a
theoretical point of view. The relativistic formulation of quantum
mechanics to be discussed later was developed by Dirac using the
Heisenberg picture. Heisenberg’s matrix mechanics like Schrödinger’s
wave mechanics was non-relativistic.
Heisenberg’s formulation of quantum mechanics also leads naturally
to the Heisenberg uncertainty principle. This principle has played
a crucial role in understanding the physical ideas behind quantum
mechanics and has in itself led to a number of developments in atomic
physics. The uncertainty principle states that it is impossible to make an
exact determination of both the momentum and position of a particle no