To demonstrate the variational principle, a trial function ψ = C₁(ψ2s+ψ3s)/(√(2)) + C₂(ψ2s-ψ3s)/(√(2)) where… · ABC26PH0270

Subject: Physical Chemistry · Chapter: Atomic Structure · Topic: Atomic Structure – General · Exam: GATE 2005-2021 · Marks: 2 · Difficulty: Medium

To demonstrate the variational principle, a trial function $\psi = C_1\frac{\psi_{2s}+\psi_{3s}}{\sqrt{2}} + C_2\frac{\psi_{2s}-\psi_{3s}}{\sqrt{2}}$ where $C_1$ and $C_2$ are the variational parameters and $\psi_{2s}$ and $\psi_{3s}$ are the 2s, and 3s orbitals of the hydrogen atom, is constructed. The corresponding secular determinant for the hydrogen atom (in eV) is
(a)$\begin{vmatrix} 3.4(1+4/9)2-E & 3.4(1-4/9)/2 \\ 3.4(1-4/9)/2 & 3.4(1+4/9)2-E \end{vmatrix}$
(b)$\begin{vmatrix} 3.4(1+4/9)2-E & 3.4(1-4/9)/2 \\ 3.4(1-4/9)/2 & 3.4(1-4/9)2-E \end{vmatrix}$
(c)$\begin{vmatrix} 3.4(1+4/9)2-E & 3.4(1+4/9)/2 \\ 3.4(1-4/9)/2 & 3.4(1-4/9)2-E \end{vmatrix}$
(d)$\begin{vmatrix} 3.4(1+4/9)2-E & 0 \\ 0 & 3.4(1+4/9)2-E \end{vmatrix}$
Answer
Answer (as printed): A
Explanation
No explanation was printed for this question.

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