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The study of exact quasi-normal modes [QNMs], and their associated quasi-normal frequencies [QNFs], has had a long and convoluted history - replete with many rediscoveries of previously known results.
T. Tietz, “Negative Hydrogen Ion”, J. Chem. Phys. 35
1917
Earlier work this paper cites.
P. M. Morse, “Diatomic molecules according to the wave mechanics. II. vibrational levels”, Phys. Rev. 34
1929
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C. Eckart, “The penetration of a potential barrier by electrons”, Phys. Rev. 35
1930
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N. Rosen and P. M. Morse, “On the vibrations of polyatomic molecules”, Phys. Rev. 42
1932
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G. Pöschl and E. Teller, “Bemerkungen zur Quantenmechanik des anharmonischen Oszillators”, Z. Phys, 83
1933
Earlier work this paper cites.
M. F. Manning and N. Rosen, “A potential function for the vibrations of diatomic molecules”, Phys. Rev. 44
1933
Earlier work this paper cites.
M. F. Manning, “Exact solutions of the Schrodinger equation”, Phys. Rev. 48
1935
Earlier work this paper cites.
L. Hulthen, “Über die Eigenlösungen der Schrödingergleichung des Deuterons”, Ark. Mat. Astron. Fys, 28A
1942
Earlier work this paper cites.
P. M. Morse and H. Feshbach, Methods of Theoretical Physics , (McGraw-Hill, New York, 1953)
1953
Earlier work this paper cites.
L. I. Schiff, Quantum Mechanics , (McGraw-Hill, New York, 1955)
1955
Earlier work this paper cites.
A. Messiah, Quantum Mechanics , (North-Holland, Amsterdam, 1958)
1958
Earlier work this paper cites.
G. Baym, Lectures on Quantum Mechanics , (Benjamin, New York, 1969)
1969
Earlier work this paper cites.
E. Merzbacher, Quantum Mechanics , (Wiley, New York, 1970)
1970
Earlier work this paper cites.
L. D. Landau and E.M. Lifshitz, Quantum Mechanics: Non-relativistic theory , (Pergamon, New York, 1977)
1977
Earlier work this paper cites.
R. Shankar, Principles of Quantum Mechanics , (Plenum, New York, 1980)
1980
Earlier work this paper cites.
N. D. Birell and P. C. W. Davies, Quantum fields in curved space , (Cambridge University Press, Cambridge, 1982)
1982
Earlier work this paper cites.
A. Z. Capri, Nonrelativistic Quantum Mechanics , (Benjamin/Cummings, Menlo Park, 1985)
1985
Earlier work this paper cites.
A. Galindo and P. Pascual, Quantum Mechanics I , (Springer-Verlag, Berlin, 1990)
1990
Cited alongside, same era.
W. Hua, “Four-parameter exactly solvable potential for diatomic molecules”, Phys. Rev. A 42
1990
Cited alongside, same era.
G. A. Natanson, “Comment on: Four-parameter exactly solvable potential for diatomic molecules”, Phys. Rev. A 44
1991
Cited alongside, same era.
R. M. Corless, G. H. Gonnet, D. E. G. Hare, and D. J. Jeffrey, “Lambert’s W Function in Maple”, Maple Technical Newsletter 9, Spring 1993, pp. 12–22
1993
Cited alongside, same era.
S. Gasiorowicz, Quantum Physics , (Wiley, New York, 1996)
1996
Cited alongside, same era.
R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, and D. E. Knuth, “On the Lambert W W function”, Adv. Computational Maths. 5
J. Natario and R. Schiappa, “On the classification of asymptotic quasinormal frequencies for d d -dimensional black holes and quantum gravity”, Adv. Theor. Math. Phys. 8
2004
Later among the works it cites.
A. I. Kheyfits (2004) “Closed-form representations of the Lambert function”, Fract. Calc. Appl. Anal. 7
2004
Later among the works it cites.
S. Das and S. Shankaranarayanan, “High frequency quasi-normal modes for black-holes with generic singularities,” Class. Quant. Grav. 22
2005
Later among the works it cites.
V. V. Nesterenko, “Boundary conditions at spatial infinity for fields in Casimir calculations”, J.Phys. A39
2006
Later among the works it cites.
A. Ghosh, S. Shankaranarayanan and S. Das, “High frequency quasi-normal modes for black holes with generic singularities. II: Asymptotically non-flat spacetimes,” Class. Quant. Grav. 23
2006
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1996
Cited alongside, same era.
M. Visser, “Some general bounds for 1-D scattering”, Phys. Rev. A 59
1999
Cited alongside, same era.
K. D. Kokkotas and B. G. Schmidt, “Quasi-normal modes of stars and black holes”, Living Rev. Rel. 2
1999
Cited alongside, same era.
H. P. Nollert, “Quasinormal modes: the characteristic ‘sound’ of black holes and neutron stars”, Class. Quant. Grav. 16
1999
Cited alongside, same era.
H. R. Beyer, “On the Completeness of the Quasinormal Modes of the Poeschl-Teller Potential”, Commun. Math. Phys. 204
1999
Cited alongside, same era.
B. H. Brandsen and C. J. Joachain, Quantum Mechanics , (Prentice Hall, New York, 2000)
2000
Cited alongside, same era.
R. L. Liboff, Introductory Quantum Mechanics , (Addison Wesley, San Francisco, 2003)
2003
Cited alongside, same era.
Later among the works it cites.
P. Boonserm and M. Visser, “Bounding the Bogoliubov coefficients”, Annals of Physics 323
2008
Later among the works it cites.
P. Boonserm and M. Visser, “Bounding the greybody factors for Schwarzschild black holes”, Phys. Rev. D 78
2008
Later among the works it cites.
V.V. Nesterenko, A. Feoli, G. Lambiase, and G. Scarpetta, “Electromagnetic shape resonances of a dielectric sphere and radiation of portable telephones”, Mod. Phys. Lett. B, 22
2008
Later among the works it cites.
P. Boonserm, “Rigorous bounds on Transmission, Reflection, and Bogoliubov coefficients”, PhD Thesis, Victoria University of Wellington, 2009, arXiv: 0907.0045 [math-ph]. (See especially chapter 3 for a discussion of the convoluted history of the Eckart potential.)
2009
Later among the works it cites.
P. Boonserm and M. Visser, “Transmission probabilities and the Miller–Good transformation”, Journal of Physics A: Mathematical and Theoretical 42
2009
Later among the works it cites.
2009
Later among the works it cites.
P. Boonserm and M. Visser, “Analytic bounds on transmission probabilities”, Annals of Physics 325
2010
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2010
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J. Skakala and M. Visser, “Semi-analytic results for quasi-normal frequencies”, JHEP 1008
2010
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2010
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