Anatomy of a Quantum Jump

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Ever since Bohr's original introduction of the quantum theory, the precise nature of transitions between discrete energy levels, with the concomitant absorption or emission of photons, has been a matter of continuing controversy. The deep philosophical issues arising from this question have been discussed in great detail by Schrödinger [1] and many others. A related phenomenon is the so-called collapse of the wavefunction. To greatly simplify the problem, the question is whether the transitions, known as quantum jumps, are truly instantaneous. Current thinking appears to be tending to the view that, to satisfy the requirements of a rational physical theory, such transitions must actually occur within a finite, although extremely short, time interval. We have conjectured that this interval might be approximated by the time it takes a light signal to traverse a Bohr radius: sec.


This Demonstration shows what the change in the wavefunction might look like for a hydrogen atom undergoing a transition on a timescale on the order of sec. Three different transitions are considered:

1. The fundamental Lyman-alpha transition at 121.567 nm, with a half-life of 1.6 nsec.

2. The E1 forbidden transition , with a half-life of 0.125 sec, which occurs through two photon emissions, producing 243 nm photons.

3. The transition , between levels separated by the Lamb shift, 1057 MHz.

The wavefunctions as shown are positive in the blue regions, negative in the yellow regions.


Contributed by: S. M. Blinder (December 2019)
Open content licensed under CC BY-NC-SA


The hydrogen wavefunctions, in atomic units:





[1] E. Schrödinger, "Are There Quantum Jumps?," The British Journal for the Philosophy of Science, 3(10) and 3(11), 1952 pp. 109–123 and 233–242. doi:10.1093/bjps/III.10.109 and doi:10.1093/bjps/III.11.233.


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