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DBL%20Hendrix%20small.png College chemistry, 1983

Derek Lowe The 2002 Model

Dbl%20new%20portrait%20B%26W.png After 10 years of blogging. . .

Derek Lowe, an Arkansan by birth, got his BA from Hendrix College and his PhD in organic chemistry from Duke before spending time in Germany on a Humboldt Fellowship on his post-doc. He's worked for several major pharmaceutical companies since 1989 on drug discovery projects against schizophrenia, Alzheimer's, diabetes, osteoporosis and other diseases. To contact Derek email him directly: Twitter: Dereklowe

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May 29, 2013

The Hydrogen Wave Function, Imaged

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Posted by Derek

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!

Comments (17) + TrackBacks (0) | Category: General Scientific News


1. James C on May 29, 2013 6:48 AM writes...

Ah yes, the "oh shit, we were right?!" moment.

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2. p on May 29, 2013 7:56 AM writes...

And here I thought you were showing off that you had finally nailed collimation.

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3. bcpmoon on May 29, 2013 8:06 AM writes...

I love to have kids, especially when I can explain something to them as fact what was not even a hypothesis when I was their age (a mere 30 years ago). Like a supermassive black hole in the center of our galaxy or that birds are dinosaurs. I love the future. The future is now.

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4. Helical_Investor on May 29, 2013 8:38 AM writes...

Schoolchildren will eventually grow up with ....

How Freudian is it that in first pass, I read this sentence as 'Schrodinger will eventually .....'.

Yes, I know, I should wear the reading glasses more often. But that was good for an internal chuckle.


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5. Wavefunction on May 29, 2013 8:41 AM writes...

So this is what God's pineal gland looks like.

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6. Too_picky... on May 29, 2013 8:58 AM writes...

To be correct Derek, the electron density is imaged, not the wavefunction which is merely a mathematical expedient, but an approximation to describing where electrons probably will be.

#3, a quantum mechanical description of Rydberg states was certainly a well established hypothesis much more than 30 years ago.

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7. FunWithFyziks on May 29, 2013 9:08 AM writes...

This is cool but I agree with #6. A wavefunction is a mathematical function (and a complex one at that) whose absolute square gives the probability density. You can't really "image a wavefunction".

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8. great unknown on May 29, 2013 9:25 AM writes...

#6, 7
What is being pictured is a specific probability contour described by a wave function.

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9. drug_hunter on May 29, 2013 9:32 AM writes...

Another triumph for Tony Stark! Very timely with the movie just coming out.

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10. ptm on May 29, 2013 10:49 AM writes...

Whatever is being imagined it looks like a generic 2d interference pattern.

I'd like to see some distinct orbital features if their method can indeed directly visualize them as they claim.

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11. Derek Lowe on May 29, 2013 11:11 AM writes...

#9, drug hunter: I'd be remiss if I didn't follow that up with a link to this site:

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12. Sisyphus on May 29, 2013 8:20 PM writes...

Neo: This...this isn't real?
Morpheus: What is real? How do you define real? If you’re talking about what you can feel, what you can smell, what you can taste and see, then real is simply electrical signals interpreted by your brain. This is the world that you know...

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13. Søren Furbo Skov on May 30, 2013 2:41 AM writes...

You can calculate the wave function of an isolated hydrogen atom, but not of one in a DC field. Basically, the wave function doesn't exist, as it would be favorable for the electron to tunnel away from the atom. At a low enough field, it needs to tunnel a long way for it to be favorable, so the tunneling is really slow, but it still interferes with the math involved in calculating the wave function.

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14. Simon666 on May 30, 2013 4:28 AM writes...

Download the article, go to figure 3, compare with what should be theoretically obtained and be impressed. Or NOT.

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15. sepisp on May 30, 2013 10:23 AM writes...

#10 and #14: There is a peak pattern, and that's the feature they're claiming. But, #14 is correct, it's not as impressive as it should be. Peak positions are roughly aligned, but their intensity is way off and shape is questionable. In the picture in this blog, for instance, the center should be much dimmer, while the two outer rings should have high and equal intensity. Also, the real image is much more diffuse (low contrast) than theory predicts.

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16. Manish on June 6, 2013 9:37 AM writes...

What about Isn't that also an imaging of orbitals?

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17. ray phoenix on June 9, 2013 6:14 PM writes...

I think it is. But the images from the two articles are different, suggesting to me that the data extracted is different. One appears to be probability distribution, the other an attempt to describe the outer shell at " most likely position"(??)

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