By Chien W., Hung Q.

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**Additional info for 3-D numerical study on the bending of symmetric composite laminates**

**Example text**

If one assume that such a density of electronic charge be proportional to the square of a total electronic wavefunction, with the proportionality factor again arbitrarily deﬁned, the corresponding value of a product of that proportionality factor and the square of the wavefunction might be measurable in a particular small spatial volume. Whatever the value of that proportionality factor, the product decays exponentially with distance d away from a particular atomic nucleus, so of form eÀd, but becomes zero only at an inﬁnite distance from that nucleus.

95 for bond stretching modes, is typically applied to each calculated harmonic wavenumber to aid a comparison with experiment. In that sense, despite its purely ﬁctitious nature, the harmonic oscillator is a valuable armament in a chemists arsenal of mathematical methods that constitute computational spectrometry to attack a dearth of infor mation about a particular molecular structure. An alternative and accurate calcu lation of wavenumbers for anharmonic vibrational modes is at present an operation far from routine, and computationally expensive; when distinguishing among similar structures, such intensive calculation is necessary.

The energies E(R) possessed by this system that depend on the internuclear distance become a potential energy V(R) for the motion of the nuclei in the ﬁeld of the electrons. If the two atomic centers could be considered to have no internal structure, their energies would become calculated from this Hamiltonian [20], O ðRÞ ¼ ^p2 =ð2 mÞ þ h2 J ð J þ 1Þ=ð2 m R2 Þ þ VðRÞ H ð1:42Þ which contains terms for the kinetic energy of vibration of those atomic centers along a line joining them, the kinetic energy of those atomic centers perpendicular to that line that corresponds to a rotation of the diatomic species about the center of mass, and the potential energy resulting from E(R) calculated with the preceding Ham iltonian; reduced mass m is deﬁned as the product of the atomic masses divided by their sum, MaMb/(Ma þ Mb).

### 3-D numerical study on the bending of symmetric composite laminates by Chien W., Hung Q.

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