4. Consider the following trial function for the ground state of the He atom: =e-a(r₁² +r₂²) In this function, a is a va

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4 Consider The Following Trial Function For The Ground State Of The He Atom E A R R In This Function A Is A Va 1 (91.81 KiB) Viewed 55 times

4. Consider the following trial function for the ground state of the He atom: =e-a(r₁² +r₂²) In this function, a is a variational parameter. (a) Write down the complete expression for determining the trial energy in a variational calculation. Be sure to indicate the volume element, integration limits, and the Hamiltonian. a) < $\H\þ> _ [$*Hodt <E> <$|4> So*odt ħ² e² 2 2 + Where, H = -(V² + V² ) - 2me 4+€071 1₂ |1₁-1₂| dt = d³r₁d³r₂ Such that, d³r = r²sin@drdəd JE b) For optimum value of a it must satisfy the condition - = 0. δα And the resulting optimum energy will be obtained after substituting the value of α, JE obtained from the condition -= 0, back into the energy equation. da (b) What is the optimum value of a and the resulting optimum energy?