Eigenvalue problems for the complex PT-symmetric potential V ( x ) = i g x
The spectrum of complex PT-symmetric potential, V ( x ) = i g x , is known to be null. We enclose this potential in a hard-box: V ( | x | ⩾ 1 ) = ∞ and in a soft-box: V ( | x | ⩾ 1 ) = 0 . In the former case, we find real discrete spectrum and the exceptional points of the potential. The asymptotic...
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| Published in | Physics letters. A Vol. 364; no. 1; pp. 12 - 16 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
16.04.2007
|
| Subjects | |
| Online Access | Get full text |
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| Summary: | The spectrum of complex PT-symmetric potential,
V
(
x
)
=
i
g
x
, is known to be null. We enclose this potential in a hard-box:
V
(
|
x
|
⩾
1
)
=
∞
and in a soft-box:
V
(
|
x
|
⩾
1
)
=
0
. In the former case, we find real discrete spectrum and the exceptional points of the potential. The asymptotic eigenvalues behave as
E
n
∼
n
2
. The solvable purely imaginary PT-symmetric potentials vanishing asymptotically known so far do not have real discrete spectrum. Our solvable soft-box potential possesses two real negative discrete eigenvalues if
|
g
|
<
(
1.22330447
)
. The soft-box potential turns out to be a scattering potential not possessing reflectionless states. |
|---|---|
| ISSN: | 0375-9601 1873-2429 |
| DOI: | 10.1016/j.physleta.2006.11.057 |