Universal Forms for One-Dimensional Quantum Hamiltonians: A Comparison of the SUSY and the De La Peña Factorization Approaches

We show that by linking two factorization techniques often employed to solve Schroedinger's equation one can give any one-dimensional hamiltonian the same form in terms of quantities typical of these approaches. These are the supersymmetric technique (SUSY) and the one of De La Pena's. It is shown that the linkage between them exhibits interesting peculiarities, that are illustrated in the case of a very important family of quantum potentials, namely, reflection-less ones.

[1]  Georg Junker.  Supersymmetric Methods in Quantum and Statistical Physics , 1996 .

[2]  A. Khare,et al.  Supersymmetry in Quantum Mechanics , 2001 .

[3]  C. Sukumar.  Supersymmetry, potentials with bound states at arbitrary energies and multi-soliton configurations , 1986 .

[4]  F. Esposito,et al.  Theory and applications of the sine-gordon equation , 1971 .

[5]  A. Wipf,et al.  Derivation of the S-matrix using supersymmetry , 1988 .

[6]  R. Montemayor,et al.  RAISING AND LOWERING OPERATORS AND SPECTRAL STRUCTURE - A CONCISE ALGEBRAIC TECHNIQUE , 1980 .

[7]  A. Khare.  Supersymmetry in quantum mechanics , 2004, math-ph/0409003.

[8]  J. Lekner.  Reflectionless eigenstates of the sech2 potential , 2007 .

[9]  T. E. Hull,et al.  The factorization method , 1951 .

[10]  E. Witten.  Search for a realistic Kaluza-Klein theory , 1981 .

[11]  R. Rajaraman.  Some non-perturbative semi-classical methods in quantum field theory (a pedagogical review)☆ , 1975 .

[12]  A. Andrianov,et al.  SECOND ORDER DERIVATIVE SUPERSYMMETRY, q DEFORMATIONS AND THE SCATTERING PROBLEM , 1995 .

[13]  B. Bagchi.  Supersymmetry In Quantum and Classical Mechanics , 2000 .

[14]  S. Takeno,et al.  Numerical Evidence of the Existence of Approximate Kink-Antikink States and Breather-Like Modes in Sine-Form Discrete Double Sine-Gordon Equation , 1985 .

[15]  Amado,et al.  Supersymmetric quantum mechanics, phase equivalence, and low energy scattering anomalies. , 1991, Physical review. C, Nuclear physics.

[16]  Avinash Khare,et al.  Supersymmetry and quantum mechanics , 1995 .

[17]  Baye.  Supersymmetry between deep and shallow nucleus-nucleus potentials. , 1987, Physical review letters.

[18]  W. Schiesser,et al.  Sine-Gordon Equation , 2011 .

[19]  A. Comtet,et al.  Anomalous behaviour of the witten index-exactly soluble models , 1984 .

[20]  D. Boyanovsky,et al.  Fractional indices in supersymmetric theories , 1984 .