  As is known, the ground state (GS) of a system of spinless bosons must be
non-degenerate and must be described by a nodeless wave function. With the help
of the general quantum mechanical analysis we show that any
\textit{anisotropic} state of a system of spinless bosons is degenerate. We
prove this for a two-dimensional (2D) system, infinite or finite circular, and
for a three-dimensional (3D) system, infinite or finite ball-shaped. It is
natural to expect that this is valid for finite 2D and 3D systems of any shape.
Hence, GS of a Bose system of any density is isotropic and, therefore,
corresponds to a liquid or gas. Therefore, the lowest state of a 2D or 3D
natural crystal consisting of spinless bosons should be described by a wave
function with nodes. This leads to nontrivial experimental predictions. We
propose a possible ansatz for the wave function of the lowest state of a 3D
Bose crystal and discuss possible experimental consequences.
