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Linear Canonical Transformations and Their Unitary Representations
We show that the group of linear canonical transformations in a 2N‐dimensional phase space is the real symplectic group Sp(2N), and discuss its unitary representation in quantum mechanics when the N
Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
We construct two new exactly solvable potentials giving rise to bound-state solutions to the Schrodinger equation, which can be written in terms of the recently introduced Laguerre- or Jacobi-type X1
Revisiting (quasi-)exactly solvable rational extensions of the Morse potential
The construction of rationally-extended Morse potentials is analyzed in the framework of first-order supersymmetric quantum mechanics. The known family of extended potentials $V_{A,B,{\rm ext}}(x)$,
EXCHANGE OPERATOR FORMALISM FOR AN INFINITE FAMILY OF SOLVABLE AND INTEGRABLE QUANTUM SYSTEMS ON A PLANE
The exchange operator formalism in polar coordinates, previously considered for the Calogero–Marchioro–Wolfes problem, is generalized to a recently introduced, infinite family of exactly solvable and
Deformed shape invariance and exactly solvable Hamiltonians with position-dependent effective mass
Known shape-invariant potentials for the constant-mass Schrodinger equation are taken as effective potentials in a position-dependent effective mass (PDEM) one. The corresponding shape-invariance
Bohr Hamiltonian with deformation-dependent mass term for the Davidson potential
Dennis Bonatsos, P. E. Georgoudis, D. Lenis, N. Minkov, and C. Quesne Institute of Nuclear Physics, National Centre for Scientific Research “Demokritos”, GR-15310 Aghia Paraskevi, Attiki, Greece
Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics
New exactly solvable rationally-extended radial oscillator and Scarf I potentials are generated by using a constructive supersymmetric quantum mechanical method based on a reparametrization of the
Canonical Transformations and Matrix Elements
We use the ideas on linear canonical transformations developed previously to calculate the matrix elements of the multipole operators between single‐particle states in a three‐dimensional oscillator
Extending Romanovski polynomials in quantum mechanics
Some extensions of the (third-class) Romanovski polynomials (also called Romanovski/pseudo-Jacobi polynomials), which appear in bound-state wavefunctions of rationally-extended Scarf II and
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