An analysis and application of the supersymmetry ͑SUSY͒ in nonrelativistic quantum mechanics involving two-component wave functions for a stability equation corresponding to two coupled real scalar fields is considered. A general positive potential for two coupled real scalar fields in 1ϩ1 dimensions with a SUSY form is investigated in which the associated two-component normal modes are non-negative, which leads to classically stable soliton solutions, and an example is explicitly considered.

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Supersymmetry (SUSY) in non-relativistic quantum mechanics (QM) is applied to a 2-dimensional physical system: a neutron in an external magnetic field. The superpotential and the two-component wave functions of the ground state are found out.

Bianchi type-I exact solutions are obtained in two models involving nonminimal coupling of gravitation and other fields.

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Using the so(2,1) Lie algebra and the Baker–Campbell–Hausdorff formulas, the Green’s function for the Hartmann potential is constructed and its bound state energy spectrum is found. Also, this Green’s function is constructed in a coherent state basis and the equivalence of the two descriptions is shown.

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