AbstractA new variation theory based on the behavior of function vector in a dual vector space is presented. The procedure is applicable to any quantum mechanical eigenvalue‐eigenvector problem and gives appropriate solution even with crude numerical integration to save computational cost. The theory offers an absolute measure of propriety for the assigned trial function. Applications on a free particle with a definite momentum, a particle in a one‐dimensional box with a definite energy, the one‐dimensional harmonic oscillator, and the ground state of helium atom are shown to demonstrate the merits of the t