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Determine whether or not the particle is in an eigenstate of Lz.

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A particle is confined in a cubic bow with edge of length a, with V=0 inside the box. The particle is in its ground state, determine whether or not the particle is in an eigenstate of Lz.

I do not know how to do this, eigenstate? Detailed solution needed, please.

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A particle is confined in a cubic bow with edge of length a, with V=0 inside the box. The particle is in its ground state, determine whether or not the particle is in an eigenstate of Lz.

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It certainly is NOT for the following reason.

First, we note that the ground state in a cube

-a/2 < x < a/2
-a/2 < y < a/2
-a/2 < z < a/2

is the product of half-wavelength cosines

ψ = const * cos(πx/2a) * cos(πy/2a) * cos(πz/2a) ...

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