Aharonov–Berry superoscillations in the radial harmonic oscillator potential
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Aharonov, Y., Albert, D., Vaidman, L.: How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. Phys. Rev. Lett. 60, 1351–1354 (1988)
Aharonov, Y., Colombo, F., Nussinov, S., Sabadini, I., Struppa, D.C., Tollaksen, J.: Superoscillation phenomena in $$SO(3)$$. Proc. R. Soc. A. 468, 3587–3600 (2012)
Aharonov, Y., Colombo, F., Sabadini, I., Struppa, D.C., Tollaksen, J.: On the Cauchy problem for the Schrödinger equation with superoscillatory initial data. J. Math. Pures Appl. 99, 165–173 (2013)
Aharonov, Y., Colombo, F., Sabadini, I., Struppa, D.C., Tollaksen, J.: Some mathematical properties of superoscillations. J. Phys. A 44, 365304 (2011). (16pp)
Aharonov, Y., Colombo, F., Sabadini, I., Struppa, D.C., Tollaksen, J.: Superoscillating sequences as solutions of generalized Schrodinger equations. J. Math. Pures Appl. 103, 522–534 (2015)
Aharonov, Y., Colombo, F., Sabadini, I., Struppa, D.C., Tollaksen, J.: Superoscillating sequences in several variables. J. Fourier Anal. Appl. 22, 751–767 (2016)
Aharonov, Y., Colombo, F., Sabadini, I., Struppa, D.C., Tollaksen, J.: The mathematics of superoscillations. Mem. Am. Math. Soc. 247(1174), v+107 (2017)
Aharonov, Y., Colombo, F., Sabadini, I., Struppa, D.C., Tollaksen, J.: How superoscillating tunneling waves can overcome the step potential (2019) (preprint)
Aharonov, Y., Colombo, F., Struppa, D.C., Tollaksen, J.: Schrödinger evolution of superoscillations under different potentials. Quantum Stud. Math. Found. 5, 485–504 (2018)
Aharonov, Y., Rohrlich, D.: Quantum Paradoxes: Quantum Theory for the Perplexed. Wiley-VCH, Weinheim (2005)
Aharonov, Y., Sabadini, I., Tollaksen, J., Yger, A.: Classes of superoscillating functions. Quantum Stud. Math. Found. 5, 439–454 (2018)
Aharonov, Y., Vaidman, L.: Properties of a quantum system during the time interval between two measurements. Phys. Rev. A 41, 11–20 (1990)
Aoki, T., Colombo, F., Sabadini, I., Struppa, D.C.: Continuity theorems for a class of convolution operators and applications to superoscillations. Ann. Mat. Pura Appl. 197, 1533–1545 (2018)
Aoki, T., Colombo, F., Sabadini, I., Struppa, D.C.: Continuity of some operators arising in the theory of superoscillations. Quantum Stud. Math. Found. 5, 463–476 (2018)
Berenstein, C.A., Gay, R.: Complex Variables. An Introduction. Graduate Texts in Mathematics, vol. 125, p. xii+650. Springer, New York (1991)
Berry, M.V.: Evanescent and real waves in quantum billiards and Gaussian beams. J. Phys. A. 27, 391 (1994)
Berry, M.: Exact nonparaxial transmission of subwavelength detail using superoscillations. J. Phys. A 46, 205203 (2013)
Berry, M.: Faster than Fourier, 1994, in Quantum Coherence and Reality. In: Anandan, J.S., Safko, J.L. (eds.) Celebration of the 60th Birthday of Yakir Aharonov, pp. 55–65. World Scientific, Singapore (1994)
Berry, M.: Representing superoscillations and narrow Gaussians with elementary functions. Milan J. Math. 84, 217–230 (2016)
Berry, M., Dennis, M.R.: Natural superoscillations in monochromatic waves in D dimension. J. Phys. A 42, 022003 (2009)
Berry, M., Popescu, S.: Evolution of quantum superoscillations, and optical superresolution without evanescent waves. J. Phys. A 39, 6965–6977 (2006)
Berry, M., Pragya, P.S.: Pointer supershifts and superoscillations in weak measurements. J. Phys. A 45, 015301 (2012)
Buniy, R., Colombo, F., Sabadini, I., Struppa, D.C.: Quantum harmonic oscillator with superoscillating initial datum. J. Math. Phys. 55, 113511 (2014)
Colombo, F., Sabadini, I., Struppa, D.C., Yger, A.: Superoscillating functions and the super-shift for generalized functions. Proc. RIMS Kyoto Univ. 55, 1–24 (2019). https://doi.org/10.4171/PRIMS/55-4-1
Colombo, F., Gantner, J., Struppa, D.C.: Evolution by Schrödinger equation of Ahronov–Berry superoscillations in centrifugal potential. In: Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences, vol. 475, no. 2225, pp. 20180390 (2019). https://doi.org/10.1098/rspa.2018.0390
Ferreira, P.J.S.G., Kempf, A.: Unusual properties of superoscillating particles. J. Phys. A 37, 12067–76 (2004)
Ferreira, P.J.S.G., Kempf, A.: Superoscillations: faster than the Nyquist rate. IEEE Trans. Signal. Process. 54, 3732–3740 (2006)
Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products, 7th edn. Elsevier/Academic Press, Amsterdam (2007)
Grosche, C., Steiner, F.: Handbook of Feynman Path Integrals, Springer Tracts in Modern Physics, vol. 145, p. x+449. Springer, Berlin (1998)
Khandekar, K.C., Lawande, S.V.: Exact propagator for a time-dependent harmonic oscillator with and without a singular perturbation. J. Math. Phys. 16, 384 (1975)
Lee, D.G., Ferreira, P.J.S.G.: Superoscillations of prescribed amplitude and derivative. IEEE Trans. Signal Process. 62, 3371–3378 (2014)
Lee, D.G., Ferreira, P.J.S.G.: Superoscillations with optimal numerical stability. IEEE Sign. Proc. Lett. 21(12), 1443–1447 (2014)
Schulman, L.S.: Techniques and Applications of Path Integration. A Wiley-Interscience Publication, p. xv+359. Wiley, New York (1981)
Taylor, B.A.: Some locally convex spaces of entire functions. In: Korevaar, J., Chern, S.S., Ehrenpreis, L., Fuchs, W.H.J., Rubel, L.A. (eds.) Entire Functions and Related Parts of Analysis, Proceedings of Symposia in Pure Matehamtics, vol. 11, pp. 431–467. American Mathematical Society, Providence, RI (1968)