Is this equation nondimensionalized? the question as mentioned in title. i want to know how this equation is dimenssionless as my efforts didn't give me the answer the equation is: $$z=(L/ \hbar) \cdot \sqrt{2m \cdot (E+V_o)}$$ as i tried in draft i found : [z]=m.Kg.s^-1 but in the solution sheet it's a dimensionless quantity. where z is the dimensionless quantity \hbar is 2* \pi * h (h: planck's constant) m is the mass of particle E and Vo are the energies of the system

Note: It seems $L$ is not angular momentum, but some length.

For the SI units we have: $$ [L] = \text{m} \\\ [\hbar] = \text{J}\text{s} = (\text{kg}\cdot (\text{m}/\text{s})^2) s = \text{m}^2 \cdot \text{kg} / \text{s} $$ And $$ [m] = \text{kg} \\\ [E] = J = \text{kg}\cdot (\text{m}/\text{s})^2 \\\ \left[\sqrt{m(E+V_0)}\right]= \text{kg}\cdot (\text{m}/\text{s}) = [p] $$ Combined we get: $$ \frac{\text{m}}{\text Js} \frac{\text{kg}\cdot\text{m}}{\text{s}} =\frac{\text{J}}{\text{J}} = 1 $$