Quantum Hamilton-Jacobi formalism is used to give a proof for Gozzi's criterion, which states that for eigenstates of the supersymmetric partners, corresponding to the same energy, the difference in the number of nodes is equal to one when supersymmetry (SUSY) is unbroken and is zero when SUSY is broken. We also show that this proof is also applicable to the case, where isospectral deformation is involved. © Indian Academy of Sciences.

Sree Ranjani S.

Kapoor A.K.

Vinash Khare A.

Panigrahi P.K.

<p>Shiv Nadar University is a comprehensive, multidisciplinary, research-focused, and student-centric University offering a full range of academic programs at the undergraduate, postgraduate and doctoral level. With state-of-the-art infrastructure, the University comprises of academic wings, sophisticated labs, international standard sports facilities, amphitheaters, auditorium, conference rooms and smart classrooms. The University&rsquo;s goal is to become internationally recognized for the quality of its research and creative endeavors and their applicability to improving quality of life, generating new insights and expanding the boundaries of human knowledge creativity. Committed to excellence in teaching, research and service, the University aims to serve the higher education needs of India and the world beyond.</p>

Shiv Nadar University

Pramana - Journal of Physics

Journal of Physics A: Mathematical and Theoretical

Exceptional orthogonal polynomials, QHJ formalism and SWKB quantization condition

Complex Variables

Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux–Crum transformations

Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry

Annals of Physics

Bound states and band structure—A unified treatment through the quantum Hamilton–Jacobi approach

A quantum Hamilton-Jacobi proof of the nodal structure of the wave functions of supersymmetric partner potentials