Matrix mechanics
In 1925 W. Heisenberg introduced matrix mechanics. His work was based on the correspondence principle of Bohr, which can be formulated as follows: In the limit of the quantum numbers approaching infinity the result of quantum theory should agree with that of the classical theory.
Heisenberg considered the Bohr atom at very large orbits.
There the orbital frequency would be the radiation frequency and the atom would be like a simple linear oscillator.
From the largest orbit, where he could get answers from classical theory, he then tried to extrapolate to the inner orbits.
Heisenberg found that in his atomic theory
does not equal
, where
represents the position of a particle and
the momentum.
He postulated that
.
M. Born pointed out that Heisenberg's strange multiplication law could be understood in terms of matrix multiplication.
Together with P. Jordan he transposed Heisenberg´s theory into a systematic matrix language.
In 1926 W. Pauli applied the Heisenberg theory to the hydrogen atom problem and did not only deduce the spectrum of hydrogen
but also the additional lines produced by electric and magnetic fields.