TY - JOUR
T1 - Non-Hermitian inverted harmonic oscillator-type Hamiltonians generated from supersymmetry with reflections
AU - Mota, R. D.
AU - Ojeda-Guillén, D.
AU - Salazar-Ramírez, M.
AU - Granados, V. D.
N1 - Publisher Copyright:
© 2019 World Scientific Publishing Company.
PY - 2019/2/10
Y1 - 2019/2/10
N2 - By modifying and generalizing known supersymmetric models, we are able to find four different sets of one-dimensional Hamiltonians for the inverted harmonic oscillator. The first set of Hamiltonians is derived by extending the supersymmetric quantum mechanics with reflections to non-Hermitian supercharges. The second set is obtained by generalizing the supersymmetric quantum mechanics valid for non-Hermitian supercharges with the Dunkl derivative instead of d dx. Also, by changing the derivative d dx by the Dunkl derivative in the creation and annihilation-type operators of the standard inverted harmonic oscillator HSIO = -1 2 d2 dx2 -1 2x2, we generate the third set of Hamiltonians. The fourth set of Hamiltonians emerges by allowing a parameter of the supersymmetric two-body Calogero-type model to take imaginary values. The eigensolutions of definite parity for each set of Hamiltonians are given.
AB - By modifying and generalizing known supersymmetric models, we are able to find four different sets of one-dimensional Hamiltonians for the inverted harmonic oscillator. The first set of Hamiltonians is derived by extending the supersymmetric quantum mechanics with reflections to non-Hermitian supercharges. The second set is obtained by generalizing the supersymmetric quantum mechanics valid for non-Hermitian supercharges with the Dunkl derivative instead of d dx. Also, by changing the derivative d dx by the Dunkl derivative in the creation and annihilation-type operators of the standard inverted harmonic oscillator HSIO = -1 2 d2 dx2 -1 2x2, we generate the third set of Hamiltonians. The fourth set of Hamiltonians emerges by allowing a parameter of the supersymmetric two-body Calogero-type model to take imaginary values. The eigensolutions of definite parity for each set of Hamiltonians are given.
KW - Dunkl operators
KW - Non-Hermitian Hamiltonians
KW - inverted harmonic oscillator
KW - reflection operators
KW - supersymmetric quantum mechanics
UR - http://www.scopus.com/inward/record.url?scp=85060056431&partnerID=8YFLogxK
U2 - 10.1142/S0217732319500287
DO - 10.1142/S0217732319500287
M3 - Artículo
SN - 0217-7323
VL - 34
JO - Modern Physics Letters A
JF - Modern Physics Letters A
IS - 4
M1 - 1950028
ER -