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Position dependent mass Scarf Hamiltonians generated via the Riccati equation
Author(s) -
Cruz y Cruz S,
SantiagoCruz C
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5068
Subject(s) - mathematics , riccati equation , gravitational singularity , trigonometry , position (finance) , factorization , hamiltonian (control theory) , mathematical analysis , spectrum (functional analysis) , mathematical physics , differential equation , quantum mechanics , physics , mathematical optimization , finance , algorithm , economics
The construction of position dependent mass Scarf Hamiltonians of the trigonometric as well as the hyperbolic types is addressed by means of the factorization method and the Riccati equation. These Hamiltonians are shown to be independent of the ordering parameter of the kinetic term. Additionally, new families of Hamiltonians with the Scarf spectrum are also determined by supersymmetry. Some examples for masses with and without singularities are considered to illustrate our results.