The Quantum Perturbation Calculations With Linear Expansion Coefficient And The Discussion With Convergent Of Energy Elgenvalues

The text recommends the virial theorem and hypervirial theorem in quantum and classical mechanics, the foundation of hypervirial theorem and the most primary application, and chooses the hypervirial operator in terms of the needing with problems to induce many hypervirial formulas from it .These formulas are some recursion formulas. If the energy eigenvalues and eigenfunctions are known, it is easy to induce the k-power average recursion formulas of coordinate (or radius vector).People induced them by all kinds of means early, because the kind of formula is very important in applying. But, comparing with other means, the hypervirial theorem is the easiest mean. If the energy eigenvalues and eigenfunctions are unknown, it can simply obtain the any high rank approximation of energy eigenvalues by combining the hypervirial theorem with the Hellmann-Feynman (HF) theorem to substitute the ordinary perturbation theory. The biggest advantage of this mean is that don't need to computer the perturbation matrix element by using zero level wave function, even don't need to give out high rank amendatory result using infinite series to sum like the ordinary perturbation theory. Thus, it not only avoids many complicated integral operation, but also obtains high rank amendatory result that it is very difficult to get or can't get.In this text, the main work is that compute the two level approximation of the linear expansion coefficient using the method combining the hypervirial theorem with the Hellmann-Feynman (HF) theorem (called HVHF perturbation method) to substitute the ordinary perturbation theory, and get out an important result they are approximately equal by comparing the quantum result with the classical result. Furthermore, using quantum and classical means compute the linear expansion coefficient of pure iron. Through comparing the result, it is found that the result is more accurate by using the HVHF perturbation method. In the way, it is more clearly understood for the classic extreme limit of quantum mechanics, and further understood for the relation of the quantum and classical mechanics. The end, it enumerate different potential energy function to discuss the convergent problem of the eigenenergy.