Abstract
We have investigated bound state solutions of the Schrodinger equation for one-dimensional harmonic oscillator potential together with even number of Dirac delta functions. These point interactions are located at symmetric points x = x i and x = −x i (i = 1, 2,..., N) and they have complex conjugate strengths \(\tilde \sigma _i\) and \(\tilde \sigma _i *\), respectively. We present explicit forms of eigenfunctions and an algebraic eigenvalue equation and numerical solutions for this \(\mathcal{P}\mathcal{T}\)-symmetric Hamiltonian.
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C.M. Bender and S. Boettcher: Phys. Rev. Lett. 80 (1998) 5243.
A. Mostafazadeh: J. Phys. A.: Math. Gen. 36 (2003) 7081.
A. Mostafazadeh: J. Math. Phys. 43 (2002) 205.
S. Albeverio, F. Gesztesy, R. Hoegh-Krohn, and H. Holden: Solvable Models in Quantum Mechanics, Springer-Verlag, New York, 1988.
S. Albeverio, S. Mei, and P. Kurasov: Lett. Math. Phys. 59 (2002) 227.
M. Znojil: J. Phys. A.: Math. Gen. 36 (2003) 7639.
M. Znojil and V. Jakubsky: J. Phys. A.: Math. Gen. 38 (2005) 5041.
M.P. Avakian, G.S. Pogosyan, A.N. Sissakian, and V.M. Ter-Antonyan: Phys. Lett. A 124 (1987) No. 4, 5, 233.
S. Fassari and G. Inglese: Helv. Phys. Acta 67 (1994) 650.
S. Fassari and G. Inglese: Helv. Phys. Acta 70 (1997) 858.
O. Olendski: J Phys.: Condens. Matter 7 (1995) 5067.
R.M. Cavalcanti and C.A.A. de Carvalho: J. Phys. A 31 (1998) 2391.
O. Olendski and C.S. Kim: J Phys.: Condens. Matter 8 (1996) 2197.
R.K. Janev and Z. Maric: Phys. Lett. A 46 (1974) 313.
S. Fassari and G. Inglese: Helv. Phys. Acta 69 (1996) 130.
J. Brunig, V. Geyler, and I. Lobanov: J. Math. Phys. 45 (2004) 1267.
E. Demiralp: J. Phys. A.: Math. Gen. 38 (2005) 4783.
N.N. Lebedev: Special Functions and Their Applications, Dover Pub., Inc., New York, 1972.
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Demiralp, E. Properties of a pseudo-Hermitian Hamiltonian for harmonic oscillator decorated with Dirac delta interactions. Czech J Phys 55, 1081–1084 (2005). https://doi.org/10.1007/s10582-005-0110-2
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DOI: https://doi.org/10.1007/s10582-005-0110-2