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May 29, 2013
The Hydrogen Wave Function, Imaged
Here's another one of those images that gives you a bit of a chill down the spine. You're looking at a hydrogen atom, and those spherical bands are the orbitals in which you can find its electron. Here, people, is the wave function. Yikes.Update: true, what you're seeing are the probability distributions as defined by the wave function. But still. . .
This is from a new paper in Physical Review Letters (here's a commentary at the APS site on it). Technically, what we're seeing here are Stark states, which you get when the atom is exposed to an electric field. Here's more on how the experiment was done:
In their elegant experiment, Stodolna et al. observe the orbital density of the hydrogen atom by measuring a single interference pattern on a 2D detector. This avoids the complex reconstructions of indirect methods. The team starts with a beam of hydrogen atoms that they expose to a transverse laser pulse, which moves the population of atoms from the ground state to the 2s and 2p orbitals via two-photon excitation. A second tunable pulse moves the electron into a highly excited Rydberg state, in which the orbital is typically far from the central nucleus. By tuning the wavelength of the exciting pulse, the authors control the exact quantum numbers of the state they populate, thereby manipulating the number of nodes in the wave function. The laser pulses are tuned to excite those states with principal quantum number n equal to 30.
The presence of the dc field places the Rydberg electron above the classical ionization threshold but below the field-free ionization energy. The electron cannot exit against the dc field, but it is a free particle in many other directions. The outgoing electron wave accumulates a different phase, depending on the direction of its initial velocity. The portion of the electron wave initially directed toward the 2D detector (direct trajectories) interferes with the portion initially directed away from the detector (indirect trajectories). This produces an interference pattern on the detector. Stodolna et al. show convincing evidence that the number of nodes in the detected interference pattern exactly reproduces the nodal structure of the orbital populated by their excitation pulse. Thus the photoionization microscope provides the ability to directly visualize quantum orbital features using a macroscopic imaging device.
n=30 is a pretty excited atom, way off the ground state, so it's not like we're seeing a garden-variety hydrogen atom here. But the wave function for a hydrogen atom can be calculated for whatever state you want, and this is what it should look like. The closest thing I know of to this is the work with field emission electron microscopes, which measure the ease of moving electrons from a sample, and whose resolution has been taken down to alarming levels).
So here we are - one thing after another that we've had to assume is really there, because the theory works out so well, turns out to be observable by direct physical means. And they are really there. Schoolchildren will eventually grow up with this sort of thing, but the rest of us are free to be weirded out. I am!
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