The notion of spherically symmetric superfunctions as functions invariant under the orthosymplectic group is introduced. This leads to dimensional reduction theorems for differentiation and integration in superspace. These spherically symmetric functions can be used to solve orthosymplectically invariant Schrödinger equations in superspace, such as the (an)harmonic oscillator or the Kepler problem. Finally, the obtained machinery is used to prove the Funk–Hecke theorem and Bochner’s relations in superspace.
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