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.

In the present study, a digital holography microscope has been developed to study instantaneous 3D velocity field in a square channel of 1000 × 1000 $\mu𝑚^2$ cross-section. The flow field is seeded with polystyrene microspheres of size $d_p = 2.1$ 𝜇m. The volumetric flow rate is set equal to 20 𝜇l/min. The instantaneous 3D velocity field is obtained by correlating the particles obtained from the 3D numerical reconstruction of holograms using particle tracking velocimetry (PTV).