The finite rectangular well (FRW) has been a staple of quantum mechanics texts and classes for decades and is the subject of a rich literature. Despite being a problem about which there would apparently be not much more to be said, the FRW continues to serve as a system for introducing students to various analytic techniques and has numerous connections to current technology and research. This paper gives a survey of past and recent FRW literature, with an emphasis on pedagogical contributions directed at graphical and analytic solutions for energy eigenvalues.

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).
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(
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,
New Jersey
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1951
).
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D. J.
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(
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, and
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K. R.
Naqvi
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S.
Waldenstrøm
, “
The finite square well: Whatever is worth teaching at all is worth teaching well
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2015
).
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M.
Belloni
and
R. W.
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, “
The infinite well and Dirac delta function potentials as pedagogical, mathematical and physical models in quantum mechanics
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Phys. Rep.
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,
25
122
(
2014
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7.
D. L.
Aronstein
and
C. R.
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, Jr.
, “
Fractional wave-function revivals in the infinite square well
,”
Phys. Rev. A
55
(
6
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4526
4537
(
1997
).
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P. H.
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, “
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,”
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),
111
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).
9.
C. D.
Cantrell
, “
Bound-state energies of a particle in a finite square well: An improved graphical solution
,”
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),
107
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(
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J. J.
Murphy
, “
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(
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12.
W. C.
Elmore
, “
Eigenvalues of the square-well problem
,”
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39
(
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),
976
977
(
1971
).
13.
P. G.
Guest
, “
Graphical solutions for the square well
,”
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1175
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(
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14.
R. D.
Murphy
and
J. M.
Phillips
, “
Bound-state eigenvalues of the square well potential
,”
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44
(
6
),
574
576
(
1976
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15.
J. D.
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,”
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45
(
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),
211
(
1977
).
16.
F. M. S.
Lima
, “
A simpler graphical solution and an approximate formula for energy eigenvalues in finite square quantum wells
,”
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1019
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(
2020
).
17.
A. A.
Cottey
, “
Graphical display of the energy spectrum of a potential well
,”
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(
11
),
1700
1701
(
1972
).
18.
E. J.
Burge
, “
Improved simple graphical solution for the eigenvalues of the finite square well potential,” Eur.
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(
3
),
154
164
(
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19.
M.
Chiani
, “
A chart for the energy levels of the square quantum well
,” e-print arXiv:1610.04468v2 (
2017
).
20.
J. V.
Mallow
, “
Simple graphical solution for the finite square well with no change of variables
,”
Am. J. Phys.
64
(
8
),
1072
1073
(
1996
).
21.
B. C.
Reed
, “
A single equation for finite rectangular well energy eigenvalues
,”
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58
(
5
),
503
504
(
1990
).
22.
S.
Garrett
, “
Bound state energies of a particle in a finite square well: A simple approximation
,”
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47
(
2
),
195
196
(
1979
).
23.
B. I.
Barker
,
G. H.
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,
J. W.
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, and
G. E.
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, “
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,”
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),
1038
1042
(
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).
24.
D. W. L.
Sprung
,
H.
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, and
J.
Martorell
, “
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,”
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(
1
),
21
25
(
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).
25.
V.
Barsan
, “
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,”
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36
(
6
),
065009
(
2015
).
26.
D. L.
Aronstein
and
C. R.
Stroud
, Jr.
, “
General series solution for finite square-well energy levels for use in wave-packet studies
,”
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68
(
10
),
943
949
(
2000
).
27.
J.-F.
Bloch
and
V.
Ignatovich
, “
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,”
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69
(
11
),
1177
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(
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).
28.
O. F.
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and
D. J.
Griffiths
, “
Exact and approximate energy spectrum for the finite square well and related potentials
,”
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74
(
1
),
43
48
(
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).
29.
C. E.
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, “
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,”
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19
(
2
),
434
435
(
1978
).
30.
R.
Baltin
, “
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,”
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40a
,
379
382
(
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).
31.
D. W. L.
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,
H.
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, and
J.
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, “
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,”
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(
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),
136
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(
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).
32.
P.
Paul
and
D.
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, “
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,”
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41
(
7
),
4551
4555
(
2000
).
33.
D. L.
Aronstein
and
C. R.
Stroud
, Jr.
, “
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,”
J. Math. Phys.
41
(
12
),
8349
8350
(
2000
).
34.
S.
Singh
,
P.
Pathak
, and
V. A.
Singh
, “
Approximate approaches to the one-dimensional finite potential well
,”
Eur. J. Phys.
32
(
6
),
1701
1710
(
2011
).
35.
M. F.
Crommie
,
C. P.
Lutz
, and
D. M.
Eigler
, “
Confinement of electrons to quantum corrals on a metal surface
,”
Science
262
(
5131
),
218
220
(
1993
).
36.
R. M.
Kolbas
and
N.
Holonyak
, Jr.
, “
Man-made quantum wells: A new perspective on the finite square-well problem
,”
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52
(
5
),
431
437
(
1984
).
37.
T. B.
Boykin
and
G.
Klimeck
, “
The discretized Schrödinger equation for the finite square well and its relationship to solid-state physics
,”
Eur. J. Phys.
26
(
5
),
865
881
(
2005
).
38.
A.
Venugopalan
and
G. S.
Agarwal
, “
Superrevivals in the quantum dynamics of a particle confined in a finite square-well potential
,”
Phys. Rev. A
59
(
2
),
1413
1422
(
1999
).
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