ABC26PH1279 · Quantum Chemistry

Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Variation Method · Exam: NET JUNE 2016 · Marks: 2 · Difficulty: Medium

Choosing some Hamiltonian H and an orthonormal basis, a linear variation is carried out to get approximately energies $\overline{\mathrm{E}}_{\mathrm{j}}$ With 2 basis functions, one obtains $\mathrm{E}_{1}(2) \leq \mathrm{E}_{2}(2)$. Taking 3 basis functions, similarly three ordered energies $\mathrm{E}_{1}(3) \leq \mathrm{E}_{2}(3) \leq$ are found. The relation which holds from the following is?
(a)$\overline{\mathrm{E}}_{1}(2) \leq \overline{\mathrm{E}}_{1}(3) \quad \overline{\mathrm{E}}_{2}(2) \leq \overline{\mathrm{E}}_{2}(3)$
(b)$\overline{\mathrm{E}}_{1}(3) \leq \overline{\mathrm{E}}_{1}(2) \quad \overline{\mathrm{E}}_{2}(2) \leq \overline{\mathrm{E}}_{2}(3)$
(c)$\overline{\mathrm{E}}_{1}(2) \leq \overline{\mathrm{E}}_{1}(3) \quad \overline{\mathrm{E}}_{2}(3) \leq \overline{\mathrm{E}}_{2}(2)$
(d)$\overline{\mathrm{E}}_{1}(3) \leq \overline{\mathrm{E}}_{1}(2) \overline{\mathrm{E}}_{2}(3) \leq \overline{\mathrm{E}}_{2}(2)$
Answer
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Explanation
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