TY - JOUR
T1 - Exact results for the infinite supersymmetric extensions of the infinite square well
AU - Gutierrez, K.
AU - León, E.
AU - Belloni, M.
AU - Robinett, R. W.
N1 - Publisher Copyright:
© 2018 European Physical Society.
PY - 2018/10/3
Y1 - 2018/10/3
N2 - One-dimensional potentials defined by (for integer S) arise in the repeated supersymmetrization of the infinite square well, here defined over the region (0, a). We review the derivation of this hierarchy of potentials and then use the methods of supersymmetric quantum mechanics, as well as more familiar textbook techniques, to derive compact closed-form expressions for the normalised solutions, , for all V (S)(x) in terms of well-known special functions in a pedagogically accessible manner. We also note how the solutions can be obtained as a special case of a family of shape-invariant potentials, the trigonometric Pöschl-Teller potentials, which can be used to confirm our results. We then suggest additional avenues for research questions related to, and pedagogical applications of, these solutions, including the behaviour of the corresponding momentum-space wave functions for large and general questions about the supersymmetric hierarchies of potentials which include an infinite barrier.
AB - One-dimensional potentials defined by (for integer S) arise in the repeated supersymmetrization of the infinite square well, here defined over the region (0, a). We review the derivation of this hierarchy of potentials and then use the methods of supersymmetric quantum mechanics, as well as more familiar textbook techniques, to derive compact closed-form expressions for the normalised solutions, , for all V (S)(x) in terms of well-known special functions in a pedagogically accessible manner. We also note how the solutions can be obtained as a special case of a family of shape-invariant potentials, the trigonometric Pöschl-Teller potentials, which can be used to confirm our results. We then suggest additional avenues for research questions related to, and pedagogical applications of, these solutions, including the behaviour of the corresponding momentum-space wave functions for large and general questions about the supersymmetric hierarchies of potentials which include an infinite barrier.
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U2 - 10.1088/1361-6404/aadc7f
DO - 10.1088/1361-6404/aadc7f
M3 - Article
AN - SCOPUS:85055866818
SN - 0143-0807
VL - 39
JO - European Journal of Physics
JF - European Journal of Physics
IS - 6
M1 - 065404
ER -