REFERENCES
1.
R. S.
Bhalerao
and Budh
Ram
, “Fun and frustration with quarkonium in a dimension
,” Am. J. Phys.
69
, 817
–818
(2001
).2.
Antonio S.
de Castro
, “Comment on ‘Fun and frustration with quarkonium in a dimension,’ by R. S. Bhalerao and B. Ram [Am. J. Phys. 69 (7), 817–818 (2001)]
,” Am. J. Phys.
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R. M.
Cavalcanti
, “Comment on ‘Fun and frustration with quarkonium in a dimension,’ by R. S. Bhalerao and B. Ram [Am. J. Phys. 69 (7), 817–818 (2001)]
,” Am. J. Phys.
70
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(2002
).4.
John R.
Hiller
, “Solution of the one-dimensional Dirac equation with a linear scalar potential
,” Am. J. Phys.
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–524
(2002
).5.
The solutions of the Dirac equation for the model of Ref. 1 are given in terms of the Hermite function or equivalently, the parabolic cylinder function The index ν was apparently assumed to be a positive integer in Ref. 1, which is why only one bound state was found. But ν is in general a noninteger as shown in Refs. 2,3,4.
6.
C. L.
Critchfield
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(1975
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Critchfield
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(1976
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Budh
Ram
, “Quark confining potential in relativistic equations
,” Am. J. Phys.
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(1982
).8.
The terminology such as “Lorentz scalar” in the present context is not strictly legitimate. For example, the “scalar potential” is not a Lorentz scalar because is not invariant under the Lorentz transformations. However, we adopt this commonly used terminology.
9.
F.
Cooper
, A.
Khare
, R.
Musto
, and A.
Wipf
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,” Ann. Phys. (N.Y.)
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, 1
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(1987
).10.
Y.
Nogami
and F. M.
Toyama
, “Supersymmetry aspects of the Dirac equation in one dimension with a Lorentz scalar potential
,” Phys. Rev. A
47
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(1993
).11.
In Eq. (4) has been eliminated in favor of χ or Alternatively, we can eliminate in favor of by redefining χ as This different choice of χ, which we do not use in this note, results in the same physics, that is, the same wave functions (in terms of and , and the same energy eigenvalues. In this connection, note that Eq. (2) is invariant under the simultaneous substitutions of and If there is a symmetry between positive and negative energy eigenvalues.
12.
If and if the last term of becomes singular and attractive. Then there can be a problem for in supporting bound states. We exclude such situations. Essentially the same remark applies to the of Eq. (9).
13.
F. A. B.
Coutinho
and Y.
Nogami
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(1990
).14.
L. I. Schiff, Quantum Mechanics (McGraw–Hill, New York, 1968), 3rd ed., Chap. 13.
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2003
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