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arXiv · 1607.06967

Supersymmetry of the quantum rotor

Vincent X. Genest·Luc Vinet·Guo-Fu Yu·Alexei Zhedanov
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Abstract

The quantum rotor is shown to be supersymmetric. The supercharge $Q$, whose square equals the Hamiltonian, is constructed with reflection operators. The conserved quantities that commute with $Q$ form the algebra $so(3)_{-1}$, an anticommutator version of $so(3)$. The subduced representation of $so(3)_{-1}$ on the space of spherical harmonics with total angular momentum $j$ is constructed and found to decompose into two irreducible components. Two natural bases for the irreducible representation spaces of $so(3)_{-1}$ are introduced and their overlap coefficients prove expressible in terms of orthogonal polynomials of a discrete variable called anti-Krawtchouk polynomials.

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Vincent X. Genest, Luc Vinet, Guo-Fu Yu, Alexei Zhedanov. 2016-07-23. Supersymmetry of the quantum rotor. https://arxiv.org/abs/1607.06967

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