通过详细计算表明，在准经典情况下，氢原子1/r的矩阵元的量子力学结果与它的Heisenberg矩阵元近似相等，在经典极限下，它们相同。

Expectation values of physical quantities in a wave packet involving few stationary states in an infinite square well are calculated. Explicit results show that the expectation values in the classical limit go over to the corresponding classical quantity in the form of the arithmetic mean (in mathematical term, the Fejer's average) of the partial Fourier series converging to the classical quantity. The number of the stationary states is that of the partial Fourer series in the Fejer's average. The quantum uncertainty is then demonstrated to have a classical counterpart.

An excess term exists when using hermitian form of Cartesian momentum pi (i D 1, 2, 3) in usual kinetic energy 1=(2μ)∑p2i for the rigid rotator, and the correct kinetic　energy turns to be 1=(2μ)∑(1=fi)pi fi pi where fi are dummy factors in classical mechanics and nontrivial in quantum mechanics.

An excess term exists when using hermitian form of Cartesian momentum pi (i=1, 2, 3) in usual kinetic energy 1/(2μ)∑p2/i for a particle moving on the 2D surface, and the correct kinetic energy turns to be 1/(2μ)∑1/fipi fi pi where the fi are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this paper, the explicit form of the dummy functions fi is given for some surfaces of nonspherical topology, such as toroidal surface, paraboloid of revolution, the hyperboloid of revolution of two sheets, and the hyperboloid of revolution of one sheets.

An analytic solution for Helfrich spontaneous curvature membrane model (H. Naito, M.Okuda and Ou-Yang Zhong-Can, Phys. Rev. E 48, 2304 (1993); 54, 2816 (1996)), which has a conspicuous feature of representing the circular biconcave shape, is studied. Results show that the solution in fact describes a family of shapes, which can be classified as: i) the flat plane (trivial case), ii) the sphere, iii) the prolate ellipsoid, iv) the capped cylinder, v) the oblate ellipsoid, vi) the circular biconcave shape, vii) the self-intersecting inverted circular biconcave shape, and viii) the self-intersecting nodoidlike cylinder. Among the closed shapes (ii)-(vii), a circular biconcave shape is the one with the minimum of local curvature energy.