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framework that embraced all the multifarious aspects of atomic physics. He knew the perfect man for the job, one well versed in the intricacies of both quantum physics and mathematics. As luck would have it, he too would be in Hanover, where Born was due to attend a meeting of the German Physical Society. Once there, he immediately sought out Wolfgang Pauli. Born asked his former assistant to collaborate with him. 'Yes, I know you are fond of tedious and complicated formalisms', came the reply as Pauli refused. He wanted no part in Born's plans: 'You are only going to spoil Heisenberg's physical ideas by your futile mathematics.'50 Feeling unable to make progress alone, he turned in desperation to one of his students for help.

In choosing 22-year-old Pascual Jordan, Born had unwittingly found the perfect collaborator for the task ahead. Entering the Technische Hochschule in Hanover in 1921 with the intention of studying physics, Jordan found the lectures rather poor and turned instead to mathematics. A year later he transferred to Göttingen to study physics. However, he rarely attended the lectures because they were too early in the morning, starting at either 7am or 8am. Then he met Born. Under his supervision, Jordan began to study physics seriously for the first time. 'He was not only my teacher, who in my student days introduced me to the wide world of physics – his lectures were a wonderful combination of intellectual clarity and horizon widening overview', Jordan later said of Born. 'But he was also, I want to assert, the person, who next to my parents, exerted the deepest, longest lasting influence on my life.'51

With Born as his guide, Jordan soon began concentrating on problems of atomic structure. Somewhat insecure and with a stutter, he appreciated Born's patience whenever they discussed the latest papers touching on atomic theory. Fortuitously, he had moved to Göttingen in time to attend the Bohr Festspiele and, like Heisenberg, was inspired by the lectures and the discussions that followed. After his doctoral dissertation in 1924, Jordan worked briefly with others before being asked by Born to collaborate with him on an attempt to explain the width of spectral lines. Jordan is 'exceptionally intelligent and astute and can think far more swiftly and confidently than I', Born wrote to Einstein in July 1925.52

By then Jordan had already heard of Heisenberg's latest ideas. Before he left Göttingen at the end of July, Heisenberg gave a talk to a small circle of students and friends about his attempt to construct a quantum mechanics based solely on the relations between observable properties. When Born asked him to collaborate, Jordan jumped at the chance to recast and extend Heisenberg's original ideas into a systematic theory of quantum mechanics. Unknown to Born, as he sent Heisenberg's paper to the journal Zeitschrift für Physik, Jordan was well versed in matrix theory through his background in mathematics. Applying these methods to quantum physics, in two months Born and Jordan laid the foundations for a new quantum mechanics that others would call matrix mechanics.53

Once Born identified Heisenberg's multiplication rule as a rediscovery of matrix multiplication, he quickly found a matrix formula that connected position q and momentum p using an expression that included Planck's constant: pq–qp=(ih/2)I, where I is what mathematicians call a unit matrix. It allowed the right-hand side of the equation to be written as a matrix. It was from this fundamental equation using the methods of matrix mathematics that all of quantum mechanics was constructed in the months that followed. Born was proud to be 'the first person to write a physical law in terms of non-commuting symbols'.54 But it 'was only a guess, and my attempts to prove it failed', he recalled later.55 Within days of being shown the formula, Jordan came up with the rigorous mathematical derivation. No wonder Born was soon telling Bohr that, aside from Heisenberg and Pauli, he considered Jordan 'to be the most gifted of the younger colleagues'.56

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