1 research outputs found
Quantization of Length in Spaces with Position-Dependent Noncommutativity
We present a novel approach to quantizing the length in noncommutative spaces
with positional-dependent noncommutativity. The method involves constructing
ladder operators that change the length not only along a plane but also along
the third direction due to a noncommutative parameter that is a combination of
canonical/Weyl-Moyal type and Lie algebraic type. The primary quantization of
length in canonical-type noncommutative space takes place only on a plane,
while in the present case, it happens in all three directions. We establish an
operator algebra that allows for the raising or lowering of eigenvalues of the
operator corresponding to the square of the length. We also attempt to
determine how the obtained ladder operators act on different states and work
out the eigenvalues of the square of the length operator in terms of
eigenvalues corresponding to the ladder operators. We conclude by discussing
the results obtained.Comment: 14 pages, 1 figur