Discrete density of states

• Discrete density of states considering minimum energy difference is proposed.
• Analytical DOS and NOS formulas based on Weyl conjecture are given.
• Discrete DOS and NOS functions are examined for various dimensions.
• Relative errors of analytical formulas are much better than the conventional ones.

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 flattened 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.