  By considering the quantum-mechanically minimum allowable energy interval, we
exactly count number of states (NOS) and introduce discrete density of states
(DOS) concept for a particle in a box for various dimensions. Expressions for
bounded and unbounded continua are analytically recovered from discrete ones.
Even though substantial fluctuations prevail in discrete DOS, they're almost
completely flatten out after summation or integration operation. It's seen that
relative errors of analytical expressions of bounded/unbounded continua rapidly
decrease for high NOS values (weak confinement or high energy conditions),
while the proposed analytical expressions based on Weyl's conjecture always
preserve their lower error characteristic.
