Quantum by Manjit Kumar

Author:Manjit Kumar
Language: pt
Format: mobi
Publisher: W. W. Norton & Company
Published: 2010-05-24T04:00:00+00:00

Figure 11: A wave packet formed from the superposition of a group of waves

Try as he might, there was no way for Schrödinger to prevent this dispersal of the wave packet. Since it was made up of waves that varied in wavelength and frequency, as the wave packet travelled through space it would soon begin to spread out as individual waves moved at different velocities. An almost instantaneous coming together, a localisation at one point in space, would have to take place every time an electron was detected as a particle. Secondly, when attempts were made to apply the wave equation to helium and other atoms, Schrödinger’s vision of the reality that lay beneath his mathematics disappeared into an abstract, multi-dimensional space that was impossible to visualise.

The wave function of an electron encodes everything there is to know about its single three-dimensional wave. Yet the wave function for the two electrons of the helium atom could not be interpreted as two three-dimensional waves existing in ordinary three-dimensional space. Instead the mathematics pointed to a single wave inhabiting a strange six-dimensional space. In each move across the periodic table from one element to the next, the number of electrons increased by one and an additional three dimensions were required. If lithium, third in the table, required a nine-dimensional space, then uranium had to be accommodated in a space with 276 dimensions. The waves that occupied these abstract multi-dimensional spaces could not be the real, physical waves that Schrödinger hoped would restore continuity and eliminate the quantum jump.

Nor could Schrödinger’s interpretation account for the photoelectric and Compton effects. There were unanswered questions: how could a wave packet possess electric charge? Could wave mechanics incorporate quantum spin? If Schrödinger’s wave function did not represent real waves in everyday three-dimensional space, then what were they? It was Max Born who provided the answer.

Born was nearing the end of his five-month stay in America when Schrödinger’s first paper on wave mechanics appeared in March 1926. Reading it on his return to Göttingen in April, he was taken completely ‘by surprise’ as others had been.45 The terrain of quantum physics had dramatically changed during his absence. Almost out of nowhere, Born immediately recognised, Schrödinger had constructed a theory of ‘fascinating power and elegance’.46 He was quick to acknowledge the ‘superiority of wave mechanics as a mathematical tool’, as demonstrated by the relative ease with which it solved ‘the fundamental atomic problem’ – the hydrogen atom.47 After all, it had taken someone of Pauli’s prodigious talent to apply matrix mechanics to the hydrogen atom. Born might have been taken by surprise but he was already familiar with the idea of matter waves long before Schrödinger’s paper was published.

‘A letter from Einstein directed my attention to de Broglie’s thesis shortly after its publication, but I was too much involved in our speculations to study it carefully’, Born admitted more than half a century later.48 By July 1925 he had made time to study de Broglie’s work and wrote to Einstein that ‘the wave theory of matter could be of very great importance’.

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