References for Exactly Solvable Problems in Quantum Chemistry
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2 : Larry K. Haines and David H. Roberts, One-Dimensional Hydrogen AtomAm. J. Phys. 37, 1145 (1969) [DOI: 10.1119/1.1975232]
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4 : M. Andrews, Singular potentials in one dimensionAm. J. Phys. 44, 1064 (1976) [DOI: 10.1119/1.10585]
5 : C. L. Hammer and T. A. Weber, Comments on the one-dimensional hydrogen atom [Am. J. Phys. 27, 649 (1959); Am. J. Phys. 37, 1145 (1969); Am. J. Phys. 44, 1064 (1976)]Am. J. Phys. 56, 281 (1988) [DOI: 10.1119/1.15668]
6 : M. Andrews, Comment on the "One-dimensional hydrogen atom"Am. J. Phys. 49, 1074 (1981) [DOI: 10.1119/1.12648]
7 : J. F. Gomes and A. H. Zimerman, Reply to "Comment on the 'One-dimensional hydrogen atom'"Am. J. Phys. 49, 1074 (1981) [DOI: 10.1119/1.12649]
8 : Mark Andrews, The one-dimensional hydrogen atomAm. J. Phys. 56, 776 (1988) [DOI: 10.1119/1.15476]
9 18 : G. Q. Hassoun, One- and two-dimensional hydrogen atomsAm. J. Phys. 49, 143 (1981) [DOI: 10.1119/1.12546]
10 26 : R. E. Moss, The hydrogen atom in one dimensionAm. J. Phys. 55, 397 (1987) [DOI: 10.1119/1.15144]
11 23 : Michael Martin Nieto, Hydrogen atom and relativistic pi-mesic atom in N-space dimensionsAm. J. Phys. 47, 1067 (1979) [DOI: 10.1119/1.11976]
12 : I. Richard Lapidus, One-dimensional Bohr atomAm. J. Phys. 56, 92 (1988) [DOI: 10.1119/1.15762]
13 : I. Richard Lapidus, One-dimensional hydrogen atom in an infinite square wellAm. J. Phys. 50, 563 (1982) [DOI: 10.1119/1.12805]
14 : I. Richard Lapidus, Periodic boundary conditions and the one-dimensional hydrogen atomAm. J. Phys. 52, 1151 (1984) [DOI: 10.1119/1.13751]
15 : B. Zaslow and Melvin E. Zandler, Two-Dimensional Analog to the Hydrogen AtomAm. J. Phys. 35, 1118 (1967) [DOI: 10.1119/1.1973790]
16 : Jacob Wen-Kuang Huang and Allen Kozycki, Hydrogen atom in two dimensionsAm. J. Phys. 47, 1005 (1979) [DOI: 10.1119/1.11670]
17 : Ronald Rockmore, On the isotropic oscillator and the hydrogenic atom in classical and quantum mechanicsAm. J. Phys. 43, 29 (1975) [DOI: 10.1119/1.10010]
19 : K. Eveker, D. Grow, B. Jost, C. E. Monfort III, K. W. Nelson, C. Stroh, and R. C. Witt, The two-dimensional hydrogen atom with a logarithmic potential energy functionAm. J. Phys. 58, 1183 (1990) [DOI: 10.1119/1.16249]
20 : Hugh F. Henry, Trigonometric solution of the polar function of the Schrödinger equation for hydrogenAm. J. Phys. 45, 584 (1977) [DOI: 10.1119/1.11029]
21 : G. R. Fowles, Solution of the Schrödinger Equation for the Hydrogen Atom in Rectangular CoordinatesAm. J. Phys. 30, 308 (1962) [DOI: 10.1119/1.1941997]
22 : M. Bander, C. Itzykson, Group Theory and the Hydrogen AtomRev. Modern Phys. 38, 330 (1966) [DOI: 10.1103/RevModPhys.38.330]
24 : Ashok Chattergee, Large-N expansions in quantum mechanics, atomic physics and some O(N) invariant systemsPhys. Report 186, 249 (1990) [DOI: 10.1016/0370-1573(90)90048-7]
25 : Keith Andrew and James Supplee, A hydrogenic atom in d-dimensionsAm. J. Phys. 58, 1177 (1990) [DOI: 10.1119/1.16248]
27 : James J. Klein, Eigenfunctions of the Hydrogen Atom in Momentum SpaceAm. J. Phys. 34, 1039 (1966) [DOI: 10.1119/1.1972444]
28 : Boris Podolsky and Linus Pauling, The momentum distribution in hydrogen-like atomsPhys. Rev. 34, 109 (1929) [DOI: 10.1103/PhysRev.34.109]
29 : V. Fock, Zur Theorie des WasserstoffatomsZ. Phys. 98, 145 (1935) [DOI: 10.1007/BF01336904]
30 : Tai-ichi Shibuya and Carl E. Wulfman, The Kepler Problem in Two-Dimensional Momentum SpaceAm. J. Phys. 33, 570 (1965) [DOI: 10.1119/1.1971931]
31 : Egil A. Hylleraas, Wellengleichung des Keplerproblems im ImpulsraumeZ. Phys. 74, 216 (1932) [DOI: 10.1007/BF01342375]
32 81 : O. L. de Lange and R. E. Raab, An operator solution for the hydrogen atom with application to the momentum representationAm. J. Phys. 55, 913 (1987) [DOI: 10.1119/1.14953]
33 82 142 : J. D. Newmarch and R. M. Golding, Ladder operators for some spherically symmetric potentials in quantum mechanicsAm. J. Phys. 46, 658 (1978) [DOI: 10.1119/1.11225]
34 : E. Ley-Koo and S. Mateos-Cortés, The hydrogen atom in a semi-infinite space limited by a conical boundaryAm. J. Phys. 61, 246 (1993) [DOI: 10.1119/1.17299]
35 : E. Ley-Koo and R. M. G. García-Castelán, The hydrogen atom in a semi-infinite space limited by a paraboloidal boundaryJ. Phys. A Math. Gen. 24, 1481 (1991) [DOI: 10.1088/0305-4470/24/7/021]
36 : A. F. Yano and F. B. Yano, Hydrogenic Wave Functions for an Extended, Uniformly Charged NucleusAm. J. Phys. 40, 969 (1972) [DOI: 10.1119/1.1986723]
37 : J. Zablotney, Energy levels of a charged particle in the field of a spherically symmetric uniform charge distributionAm. J. Phys. 43, 168 (1975) [DOI: 10.1119/1.9884]
38 : E. Ley-Koo, E. Castaño, D. Finotello, E. Nahmad-Achar and S. Ulloa, Alternative form of the hydrogenic wave functions for an extended, uniformly charged nucleusAm. J. Phys. 48, 949 (1980) [DOI: 10.1119/1.12365]
39 : Henry Zatzkis, Thomson AtomAm. J. Phys. 26, 635 (1958) [DOI: 10.1119/1.1934721]
40 : R. Crandall, R. Whitnell, and R. Bettega, Exactly soluble two-electron atomic modelAm. J. Phys. 52, 438 (1984) [DOI: 10.1119/1.13650]
41 89 : Soo-Y. Lee, The hydrogen atom as a Morse oscillatorAm. J. Phys. 53, 753 (1985) [DOI: 10.1119/1.14306]
42 : David S. Bateman, Clinton Boyd, and Binayak Dutta-Roy, The mapping of the Coulomb problem into the oscillatorAm. J. Phys. 60, 833 (1992) [DOI: 10.1119/1.17065]
43 : H. A. Gersch, An exactly soluble one-dimensional, two-particle problemAm. J. Phys. 52, 227 (1984) [DOI: 10.1119/1.13682]
44 : Gary Simons, Model Potential for Pseudopotential CalculationsJ. Chem. Phys. 55, 756 (1971) [DOI: 10.1063/1.1676142]
45 : E. Fues, Das Eigenschwingungsspektrum zweiatomiger Moleküle in der UndulationsmechanikAnn. Phys. 385, 367 (1926) [DOI: 10.1002/andp.19263851204]
46 : P. L. Goodfriend, Model Pseudopotentials as a Source of Useful Problems for Quantum Chemistry CoursesJ. Chem. Educ. 55, 639 (1978) [DOI: 10.1021/ed055p639]
47 : Harold N. Spector and Johnson Lee, Relativistic one-dimensional hydrogen atomAm. J. Phys. 53, 248 (1985) [DOI: 10.1119/1.14132]
48 : Paul R. Auvil and Laurie M. Brown, The relativistic hydrogen atom: A simple solutionAm. J. Phys. 46, 679 (1978) [DOI: 10.1119/1.11231]
49 : H. Gali&cced;, Fun and frustration with hydrogen in a 1+1 dimensionAm. J. Phys. 56, 312 (1988) [DOI: 10.1119/1.15630]
50 : D. M. Thomson, Geometrical Relations for Charged Particles in a Uniform Magnetic FieldAm. J. Phys. 40, 1673 (1972) [DOI: 10.1119/1.1987010]
51 : C. A. Scholl and N. H. Fletcher, Quantum cyclotronAm. J. Phys. 44, 186 (1976) [DOI: 10.1119/1.10501]
52 : D. M. Thomson, Motion of a Wave Packet Constructed from Landau Gauge SolutionsAm. J. Phys. 40, 1669 (1972) [DOI: 10.1119/1.1987009]
53 : J. Katriel and G. Adam, A System with Infinitely Degenerate Bound StatesAm. J. Phys. 37, 565 (1969) [DOI: 10.1119/1.1975689]
54 : Mark P. Silverman, An exactly soluble quantum model of an atom in an arbitrarily strong uniform magnetic fieldAm. J. Phys. 49, 546 (1981) [DOI: 10.1119/1.12670]
55 : Miguel Calvo, Quantum mechanics of a chargeless spinning particle in a periodic magnetic field: A simple, soluble systemAm. J. Phys. 55, 552 (1987) [DOI: 10.1119/1.15114]
56 : I. I. Rabi, Space Quantization in a Gyrating Magnetic FieldPhys. Rev. 51, 652 (1937) [DOI: 10.1103/56_PhysRev.51.652]
57 : J. Fernando Perez and F. A. B. Coutinho, Schrödinger equation in two dimensions for a zero-range potential and a uniform magnetic field: An exactly solvable modelAm. J. Phys. 59, 52 (1991) [DOI: 10.1119/1.16714]
58 : Lars Melander, Coulomb and Resonance Integrals in Molecular Orbital TheoryJ. Chem. Educ. 39, 343 (1962) [DOI: 10.1021/ed039p343]
59 : Edward A. Johnson and H. Thomas Williams, Quantum solutions for a symmetric double square wellAm. J. Phys. 50, 239 (1982) [DOI: 10.1119/1.13046]
60 : B. Cameron Reed, A single equation for finite rectangular well energy eigenvaluesAm. J. Phys. 58, 503 (1990) [DOI: 10.1119/1.16457]
61 : R. M. Kolbas and N. Holonyak Jr., Man-made quantum wells: A new perspective on the finite square-well problemAm. J. Phys. 52, 431 (1984) [DOI: 10.1119/1.13649]
62 : E. U. Condon and P. M. Morse, Quantum Mechanics of Collision Processes I. scattering of particles in a definite force fieldRev. Modern Phys. 3, 43 (1931) [DOI: 10.1103/RevModPhys.3.43]
63 : Paul H. Pitkanen, Rectangular Potential Well Problem in Quantum MechanicsAm. J. Phys. 23, 111 (1955) [DOI: 10.1119/1.1933912]
64 : S. W. Doescher and M. H. Rice, Infinite Square-Well Potential with a Moving WallAm. J. Phys. 37, 1246 (1969) [DOI: 10.1119/1.1975291]
65 : Mark Goodman, Path integral solution to the infinite square wellAm. J. Phys. 49, 843 (1981) [DOI: 10.1119/1.12720]
66 : Terrance C. Dymski, Agreement Between Classical and Quantum Mechanical Solutions for a Linear Potential Inside a One-Dimensional Infinite Potential WellAm. J. Phys. 36, 54 (1968) [DOI: 10.1119/1.1974411]
67 : Noble M. Johnson and John N. Churchill, Comments on "Agreement between Classical and Quantum Mechanical Solutions for a Linear Potential inside a One-Dimensional Infinite Potential Well"Am. J. Phys. 37, 1287 (1969) [DOI: 10.1119/1.1975321]
68 : Noble M. Johnson and John N. Churchill, Position Expectation Values for an Electron in an Infinite Tilted WellAm. J. Phys. 38, 487 (1970) [DOI: 10.1119/1.1976371]
69 : John N. Churchill and Floyd O. Arntz, The Infinite Tilted-Well: An Example of Elementary Quantum Mechanics with Applications toward Current ResearchAm. J. Phys.37, 693 (1969) [DOI: 10.1119/1.1975775]
70 : R. Delbourgo, On the linear potential hillAm. J. Phys. 45, 1110 (1977) [DOI: 10.1119/1.10958]
71 : F. E. Cummings, The particle in a box is not simpleAm. J. Phys. 45, 45 (1977) [DOI: 10.1119/1.10981]
72 : Ying Q. Liang, Hong Zhang, and Yves X. Dardenne, Momentum Distributions for a Particle in a BoxJ. Chem. Educ. 72, 148 (1995) [DOI: 10.1021/ed072p148]
73 : Rolf G. Winter, Construction of some soluble quantal problemsAm. J. Phys. 45, 569 (1977) [DOI: 10.1119/1.10942]
74 : Herbert Massmann, Illustration of resonances and the law of exponential decay in a simple quantummechanical problemAm. J. Phys. 53, 679 (1985) [DOI: 10.1119/1.14284]
75 : Peter Senn, Time evolutions of quantum mechanical states in a symmetric double-well potentialAm. J. Phys. 60, 228 (1992) [DOI: 10.1119/1.16900]
76 : W. Edward Gettys, Quantum Theory of a Square Well Plus Delta Function PotentialAm. J. Phys. 41, 670 (1973) [DOI: 10.1119/1.1987329]
77 : T. M. Kalotas and A. R. Lee, A new approach to one-dimensional scatteringAm. J. Phys. 59, 48 (1991) [DOI: 10.1119/1.16705]
78 : T. M. Kalotas and A. R. Lee, The bound states of a segmented potentialAm. J. Phys. 59, 1036 (1991) [DOI: 10.1119/1.16643]
79 113 : Guy Fogleman, Quantum stringsAm. J. Phys. 55, 330 (1987) [DOI: 10.1119/1.15201]
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83 : W. Edward Gettys and H. W. Graben, Quantum solution for the biharmonic oscillatorAm. J. Phys. 43, 626 (1975) [DOI: 10.1119/1.9763]
84 : William S. Porter, Oscillator in a Uniform FieldAm. J. Phys. 33, 504 (1965) [DOI: 10.1119/1.1971750]
85 : Jeff D. Chalk, Tunneling through a truncated harmonic oscillator potential barrierAm. J. Phys. 58, 147 (1990) [DOI: 10.1119/1.16223]
86 : J. L. Marin and S. A. Cruz, On the harmonic oscillator inside an infinite potential wellAm. J. Phys. 56, 1134 (1988) [DOI: 10.1119/1.15738]
87 : Paul H. E. Meijer and Tomoyasu Tanaka, Quantum Mechanics of Beats between Weakly Coupled OscillatorsAm. J. Phys. 31, 161 (1963) [DOI: 10.1119/1.1969339]
88 : Göran Grimvall and Olle Gunnarsson, Concepts in Many-Body Systems Illustrated by Coupled OscillatorsAm. J. Phys. 41, 1241 (1973) [DOI: 10.1119/1.1987536]
90 125 : Vernon W. Myers, Some Exact Solutions of the Time-Dependent Schrödinger EquationAm. J. Phys. 28, 114 (1960) [DOI: 10.1119/1.1935072]
91 : Edward H. Kerner, Note on the forced and damped oscillator in quantum mechanicsCan. J. Phys. 36, 371 (1958) [DOI: 10.1139/p58-038]
92 : R. W. Fuller, S. M. Harris, and E. Leo Slaggie, -Matrix Solution for the Forced Harmonic OscillatorAm. J. Phys. 31, 431 (1963) [DOI: 10.1119/1.1969575]
93 : P. Carruthers and M. M. Nieto, Coherent States and the Forced Quantum OscillatorAm. J. Phys. 33, 537 (1965) [DOI: 10.1119/1.1971895]
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95 : F. Ninio, The Forced Harmonic Oscillator and the Zero-Phonon Transition of the Mössbauer EffectAm. J. Phys. 41, 648 (1973) [DOI: 10.1119/1.1987323]
96 : Bernard Yurke, Quantizing the damped harmonic oscillatorAm. J. Phys. 54, 1133 (1986) [DOI: 10.1119/1.14730]
97 : William Band, Forced Vibrations of a Harmonic Lattice in Quantum MechanicsAm. J. Phys. 30, 646 (1962) [DOI: 10.1119/1.1942151]
98 : C. F. Lo, An aging harmonic oscillatorAm. J. Phys. 56, 827 (1988) [DOI: 10.1119/1.15459]
99 : C. Eftimiu, Exactly solvable three-dimensional scattering problemAm. J. Phys. 51, 709 (1983) [DOI: 10.1119/1.13151]
100 : I. Richard Lapidus, Interaction of a charge and an electric dipole in one dimensionAm. J. Phys. 48, 51 (1980) [DOI: 10.1119/1.12240]
101 : Stephen K. Knudson, of a simple inelastic scattering problemAm. J. Phys. 43, 964 (1975) [DOI: 10.1119/1.10021]
102 : J. G. Loeser, H. Rabitz, A. E. DePristo, and E. A. Rohlfing, A simple model for inelastic scatteringAm. J. Phys. 49, 1046 (1981) [DOI: 10.1119/1.12580]
103 : A. H. Kahn, Phase-Shift Method for One-Dimensional ScatteringAm. J. Phys. 29, 77 (1961) [DOI: 10.1119/1.1937700]
104 : Joseph B. Keller, Uniform solutions for scattering by a potential barrier and bound states of a potential wellAm. J. Phys. 54, 546 (1986) [DOI: 10.1119/1.14560]
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107 : Clinton DeW. Van Siclen, Scattering from an attractive delta-function potentialAm. J. Phys. 56, 278 (1988) [DOI: 10.1119/1.15667]
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109 : Waikwok Kwong, Jonathan L. Rosner, Jonathan F. Schonfeld, C. Quigg, and H. B. Thacker, Degeneracy in one-dimensional quantum mechanicsAm. J. Phys. 48, 926 (1980) [DOI: 10.1119/1.12203]
110 : Lawrence H. Buch and Harry H. Denman, Solution of the Schrödinger Equation for Some Electric Field ProblemsAm. J. Phys. 42, 304 (1974) [DOI: 10.1119/1.1987677]
111 : M. M. Moya and J. S. Helman, Analytical and numerical solution of the Schrödinger equation for a surface potential barrier including spin-orbit interactionAm. J. Phys. 47, 452 (1979) [DOI: 10.1119/1.11815]
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114 : R. Aldrovandi and P. Leal Ferreira, Quantum pendulumAm. J. Phys. 48, 660 (1980) [DOI: 10.1119/1.12332]
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126 : O. L. de Lange, An operator solution for the Hulthén potentialAm. J. Phys. 59, 151 (1991) [DOI: 10.1119/1.16596]
127 : Jeff D. Chalk, A study of barrier penetration in quantum mechanicsAm. J. Phys. 56, 29 (1988) [DOI: 10.1119/1.15425]
128 : Budh Ram, Quark confining potential in relativistic equationsAm. J. Phys. 50, 549 (1982) [DOI: 10.1119/1.12820]
129 : K. R. Brownstein, Calculation of a bound state wavefunction using free state wavefunctions onlyAm. J. Phys. 43, 173 (1975) [DOI: 10.1119/1.9892]
130 : Mark J. Thomson and Bruce H. J. McKellar, The solution of the Dirac equation for a high square barrierAm. J. Phys. 59, 340 (1991) [DOI: 10.1119/1.16546]
131 : Avinash Khare and Rajat K. Bhaduri, Exactly solvable noncentral potentials in two and three dimensionsAm. J. Phys. 62, 1008 (1994) [DOI: 10.1119/1.17698]
132 : Bill Sutherland, Exact Results for a Quantum Many-Body Problem in One DimensionPhys. Rev. A 4, 2019 (1971) [DOI: 10.1103/PhysRevA.4.2019]
133 : J. B. McGuire, Study of Exactly Soluble One-Dimensional N-Body ProblemsJ. Math. Phys. 5, 622 (1964) [DOI: 10.1063/1.1704156]
134 : M. A. Gregório and A. S. de Castro, A particle moving in a homogeneous time-varying forceAm. J. Phys. 52, 557 (1984) [DOI: 10.1119/1.13620]
135 : Michael Martin Nieto, Exact wave-function normalization constants for the B0 tanhz- U0 cosh-2z and Pöschl-Teller potentialsPhys. Rev. A 17, 1273 (1978) [DOI: 10.1103/PhysRevA.17.1273]
136 : N. Rosen and Philip M. Morse, On the Vibrations of Polyatomic MoleculesPhys. Rev. 42, 210 (1932) [DOI: 10.1103/PhysRev.42.210]
137 : D. S. Onley and A. Kumar, Time dependence in quantum mechanics - Study of a simple decaying systemAm. J. Phys. 60, 432 (1992) [DOI: 10.1119/1.16897]
138 : W. Elberfeld and M. Kleber, Time-dependent tunneling through thin barriers: A simple analytical solutionAm. J. Phys. 56, 154 (1988) [DOI: 10.1119/1.15695]
139 : D. L. Weaver, Solving spin-1 problems using spin-1/2 methodsAm. J. Phys. 46, 721 (1978) [DOI: 10.1119/1.11275]
140 141 150 : Fred Cooper and Joseph N. Ginocchio, Relationship between supersymmetry and solvable potentialsPhys. Rev. D 36, 2458 (1987) [DOI: 10.1103/PhysRevD.36.2458]
143 : Dennis Aebersold, Integral Equations in Quantum ChemistryJ. Chem. Educ. 52, 434 (1975) [DOI: 10.1021/ed052p434]
144 : L. Infield and T. E. Hull, The Factorization MethodRev. Modern Phys. 23, 21 (1951) [DOI: 10.1103/RevModPhys.23.21]
145 : Ranjan Das and A. B. Sannigrahi, The Factorization Method and Its Applications in Quantum ChemistryJ. Chem. Educ. 58, 383 (1981) [DOI: 10.1021/ed058p383]
146 : J. Douglas Milner and Carl Peterson, Notes on the Factorization Method for Quantum ChemistryJ. Chem. Educ. 62, 567 (1985) [DOI: 10.1021/ed062p567]
147 : Paulo Henrique A. Santana and Abel Rosato, Use of the Laplace Transform Method to Solve the One-Dimensional Periodic-Potential ProblemAm. J. Phys. 41, 1138 (1973) [DOI: 10.1119/1.1987504]
149 : L. É. Gendenshteĩn, Derivation of exact spectra of the Schrödinger equation by means of supersymmetryJETP Lett. 38, 356 (1983) [Source: jetpletters.ac.ru/ps/1822/article_27857.shtml]
151 152 : John W. Norbury, The quantum mechanical few-body problemAm. J. Phys. 57, 264 (1989) [DOI: 10.1119/1.16050]
153 : Jan Makarewicz, Exact solvable three-dimensional models of many-body systemsAm. J. Phys. 54, 178 (1986) [DOI: 10.1119/1.14686]