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In this case, the QM model allows for probabilistic radii, not fixed radii, and the quantization is the energy level. An electron with principal quantum number n = 2 will always have quantized energy corresponding to \( E = R(1/n^2) \), but the exact minimal and maximal radial distance from the nucleus is not specified as in the Bohr model of the atom. Similar to the Bohr model though, the most probable radial distance is quantifiable, and that is the radius the electron is most likely to inhabit, however it will be found elsewhere at other times.

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Title: The dying breed of craftsmen behind the tools that make scientific research possible - LA Times

Keywords: government-funded research opened, snake glass coils, fuse glass beakers, organic chemistry, research hubs, world war, experienced glassblowers, glassblowers remain, church laboratory, befallen glassblowing, glass manufacturer, glass technicians, cost-cutting world, jobs tend, entry-level jobs

Summary: Hunkered down in the sub-basement of the Norman W. Church Laboratory for Chemical Biology, underneath a campus humming with quantum teleportation devices, gravity wave detectors and neural prosthetics, Rick Gerhart chipped away at a broken flask.<br>Peering into the dancing flames, he examined his work for wrinkles — imperfections invisible to the untrained eye.<br>“It not only should be functional,” he said, smoothing the rim with a carbon rod, “it has to look good.”<br>Here in Caltech’s one-man glass shop, where Gerhart transforms a researcher’s doodles into intricate laboratory equipment, craftsmanship is king.<br>In a cost-cutting world of machines and assembly plants, few glassblowers remain with the level of mastery needed at research hubs like Caltech.<br>“He’s a somewhat dying breed,” said Sarah Reisman, who relied on Gerhart to create 20 maze-like contraptions for her synthetic organic chemistry lab.<br>Rick Gerhart, scientific glass blower at Caltech, has been helping to make scientific research possible at the campus since 1992.<br>(Dillon Deaton/Los Angeles Times)<br>Similar fates have befallen glassblowing at UCLA and NASA’s Jet Propulsion Laboratory.<br>Across the U.S., those who land such jobs tend to stay until retirement.<br>He chuckled: “Looks like we have to steal somebody.”<br>To master scientific glassblowing, proper training and apprenticeships are key.<br>In addition to the hands-on training, which requires a knack for precision as well as coordination, students must take courses in organic chemistry, math and computer drawing.<br>So it really takes a long time to get to a position like Rick’s.”<br>Gerhart enrolled in the Salem program in 1965, after dropping out of college to give his father’s profession a try.<br>The craft, which dates back to alchemy in the 2nd century, took hold in America by the 1930s and 1940s, after World War I cut off glassware supply from Germany.<br>The profession peaked after World War II, when booms in oil and government-funded research opened up numerous glassblowing jobs in many a lab.<br>At first, Gerhart hopped around a number of firms and worked alongside more experienced glassblowers at TRW Inc. and UCLA.<br>When he settled at Caltech in 1992, the glassblower before him handed over the key to the shop and said, “Good luck.” On his own, Gerhart pieced together his patchwork of experience to twist and fuse glass beakers and snake glass coils over vacuum chambers.<br>“That’s when I really started learning.”<br>Social media videos have sparked new interest in the craft, Briening said.<br>But while his students have no trouble getting entry-level jobs at companies like Chemglass Life Sciences, a glass manufacturer, and General Electric Global Research, rarely are universities willing to budget the overhead costs for more than one glassblower, if any.<br>“Years ago, all the universities had two or three people,” Briening said.<br>One of the few resources left for the next generation is the American Scientific Glassblowers Society, a close-knit group that hosts national workshops and swaps ideas when a researcher’s custom order stumps one of its members.<br>Its members also serve as Caltech’s best — and possibly only — options once Gerhart leaves.<br>“Rick’s one of those glass technicians that I put in the top 5%,” Ponton said.<br>