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We describe five quantum mechanics experiments that have been designed for an undergraduate setting. The experiments use correlated photons produced by parametric down conversion to generate interference patterns in interferometers. The photons are counted individually. The experimental results illustrate the consequences of multiple paths, indistinguishability, and entanglement. We analyze the results quantitatively using plane-wave probability amplitudes combined according to Feynman's rules, the state-vector formalism, and amplitude packets. The apparatus fits on a 2Јϫ4Ј optical breadboard.

Using a new bunched-beam technique in the GSI heavy-ion experimental storage ring (ESR), we performed precision laser spectroscopy on relativistic heavy ions in the hitherto inaccessible infrared optical region. We determined the wavelength of the M1 transition between the F 1 ͑t ഠ 50 ms͒ and F 0 hyperfine states of the 1s ground state of hydrogenlike 207 Pb 811 . Comparing the result of 1019.7(2) nm with very recent theoretical predictions concerning QED and nuclear size contributions, a disagreement of 4.5 nm is found. Since the nucleus of 207 Pb 811 is well described by the single-particle shell model, uncertainties in nuclear corrections are expected to be small. [S0031-9007(98)07624-8] PACS numbers: 32.30.Jc, 12.20.Fv, 21.10.Ky The hyperfine splitting (HFS) of the 1s ground state of one-electron, two-body (hydrogenlike) system is the simplest and most basic magnetic interaction in atomic physics. In hydrogen the splitting is measured to thirteen significant figures, considerably more precise than the six-digit precision of the theoretical calculations of this quantity [1]. These calculations solve the Dirac equation and then add corrections for the effects of the finite size of the nuclear charge and magnetization as well as for the QED effects of self-energy and vacuum polarization. While the QED contributions are of the order of 10 26 to 10 25 for a single proton, these corrections are several percent in hydrogenlike ions of large Z in which the electron experiences exceptionally intense electric and magnetic fields. Thus measurements of the spectra of these systems can stringently test theoretical calculations of QED and nuclear effects.Recently the 1s ground state transitions in high-Z, hydrogenlike ions have become accessible to optical spectroscopy at the experimental storage ring (ESR) at GSI-Darmstadt and at the electron beam ion trap Super-EBIT at Lawrence Livermore National Laboratory. Measurements of the ground state hyperfine splittings of 209 Bi 821 at GSI [2] and 165 Ho 661 at LLNL [3] have stimulated a large number of theoretical calculations of the wavelengths of these transitions [4][5][6][7][8][9][10][11][12][13][14][15]. Discrepancies are fond between theory and experiment for both 209 Bi 821 and 165 Ho 661 .The calculations for bismuth yield a value 1 nm ͑5 3 10 23 ͒ larger than the measured value. On the basis of the precisions assigned to the corrections this discrepancy is significant, but corrections for the nuclear effects vary considerably depending upon how much the nuclear core is assumed to be polarized. For holmium, a smaller discrepancy between the calculated and measured values is reported [3], but the theoretical analysis did not take into account nuclear polarization [15] which is expected to contribute significantly.In view of this unsatisfactory situation we measured the 1s ground state hyperfine transition of 207 Pb 811 . We chose this nucleus because it is well described by the single-particle model. The magnetic moment has been measured with high precision in the ato...

We are developing materials for classroom teaching about the quantum behavior of photons in beam splitters as part of a project to create five experiments that use correlated photons to exhibit nonclassical quantum effects vividly and directly. Pedagogical support of student understanding of these experiments requires modification of the usual quantum mechanics course in ways that are illustrated by the treatment of the beam splitter presented here.