In the case of some $m$  standard (i.e., ``commuting", bosonic) and
$2n$ fermionic (i.e., anticommuting) coordinates $x$ the literature
only seems to offer some closed-form solutions of Schr\"{o}dinger
equation for harmonic oscillator and Coulomb potentials. The MS adds
the first nontrivial point-interaction model where a bound state is
known to exist at $m=1$ and $n=0$. Using the method of ref. [9] an
explicit formula for the energy and wave function of the same bound
state is found at any $n>0$ for $m=1$. At $m=0$ the problem becomes
trivial (= purely algebraic) but more levels are noticed to emerge.

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MR2432539 De Bie, Hendrik Schrödinger equation with delta potential in superspace. Phys. Lett. A 372 (2008), no. 24, 4350--4352. 81Qxx