Question:
Following trial wave functions \( \phi_1 = e^{-Z' (r_1 + r_2)} \) and \( \phi_2 = e^{-Z' (r_1 + r_2) (1 + g |\vec{r}_1 - \bar{\vec{r}}_2|)} \) are used to obtain variational estimates \( E_1 \) and \( E_2 \) for the ground state energy \( E_0 \) of the helium atom. Here, \( Z' \) and \( g \) are variational parameters, \( \bar{\vec{r}}_1 \) and \( \bar{\vec{r}}_2 \) are the position vectors of the electrons. Let \( E_0 \) be the exact ground state energy of the helium atom.\( E_1 \) and \( E_2 \) are the variational estimates of the ground state energy of the helium atom corresponding to \( \phi_1 \) and \( \phi_2 \), respectively, Which one of the following options is true?
Following trial wave functions \( \phi_1 = e^{-Z' (r_1 + r_2)} \) and \( \phi_2 = e^{-Z' (r_1 + r_2) (1 + g |\vec{r}_1 - \bar{\vec{r}}_2|)} \) are used to obtain variational estimates \( E_1 \) and \( E_2 \) for the ground state energy \( E_0 \) of the helium atom. Here, \( Z' \) and \( g \) are variational parameters, \( \bar{\vec{r}}_1 \) and \( \bar{\vec{r}}_2 \) are the position vectors of the electrons. Let \( E_0 \) be the exact ground state energy of the helium atom.\( E_1 \) and \( E_2 \) are the variational estimates of the ground state energy of the helium atom corresponding to \( \phi_1 \) and \( \phi_2 \), respectively, Which one of the following options is true?
Updated On: Jul 12, 2024
- \(E_1\leq E_0, E_2\leq E_0, E_1\geq E_2\)
- \(E_1\geq E_0, E_2\leq E_0, E_1\geq E_2\)
- \(E_1\leq E_0, E_2\geq E_0, E_1\leq E_2\)
- \(E_1\geq E_0, E_2\geq E_0, E_1\geq E_2\)
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The Correct Option is D
Solution and Explanation
The correct option is (D): \(E_1\geq E_0, E_2\geq E_0, E_1\geq E_2\)
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