For some one-electron system with l=0 and m=0, the functions N0 e- sigma and N1(2- sigma ) e- sigma refer respectively to the ground (E0 ) and fist excited (E1 ) energy levels. If a variational wave function N2(3- sigma ) e- sigma yields an average energy E, it will satisfy

ABC26PH1262 · Quantum Chemistry

Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Variation Method · Exam: NET JUNE 2014 · Marks: 2 · Difficulty: Medium

For some one-electron system with $\mathrm{l}=0$ and $\mathrm{m}=0$, the functions $\mathrm{N}_{0} \mathrm{e}^{-\sigma}$ and $\mathrm{N}_{1}(2-\sigma) \mathrm{e}^{-\sigma}$ refer respectively to the ground $\left(\mathrm{E}_{0}\right)$ and fist excited $\left(\mathrm{E}_{1}\right)$ energy levels. If a variational wave function $\mathrm{N}_{2}(3-\sigma) \mathrm{e}^{-\sigma}$ yields an average energy $\overline{\mathrm{E}}$, it will satisfy

(a)$\overline{\mathrm{E}} \geq 0$

(b)$0 \leq \overline{\mathrm{E}} \leq \mathrm{E}_{0}$

(c)$\overline{\mathrm{E}} \geq \mathrm{E}_{1}$

(d)$\mathrm{E}_{0} \leq \overline{\mathrm{E}} \leq \mathrm{E}_{1}$

Answer

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Explanation

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