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新虫 (初入文坛)

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虫号: 1073825
注册: 2010-08-13
专业: 有机化学

[求助] 量子力学问题急求帮助，在线等。

小弟初入研究生，遇到量子化学问题实在不懂，恳请哪位大侠帮忙。小弟在线等，感激涕零。
1. Find the radial wavefunction of an electron in a hydrogen atom for a 3d state

2. Using raising and lowering operators, I+, I-, find the wavefunctions of the rigid rotor d states with I= -2, -1, 0, 1, 2.

3.Estimate the energy of the ground state for Li+ ion using perturbation theory and variational method with the probe function c`exp(-（r1+r2)/a)

4. Using the same probe wavefunction as in the problem 3 estimate the ionization potential of the helium atom and compare it to the ionizaiton potential of hydrogen atom.

5.Consider charged Harmonic oscillator ( charge q, mass m, frequency w) in the external electric field, F, parallel to the oscillator displacement. What are the stationary state wavefunctions of this oscillator ( Hint: Complete the square fro the potential energy and change the variable for the cooridinate to obtain the new harmonic oscillator Hamiltonian; then express them using the known solutions for harmonic oscillator).

感谢帮忙！

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