Question

2. Use slater determinants to show that the 1st excited state of Helium atom can be expressed as below. $\frac{1}{2}$ [1s(1)2s(2)+1s(2)2s(1)][?(1)?(2)??(1)?(2)] $\frac{1}{\sqrt{2}}$ [1s(1)2s(2)?1s(2)2s(1)]?(1)?(2) $\frac{1}{2}$ [1s(1)2s(2)?1s(2)2s(1)]?(1)?(2)][?(1)?(2)+?(1)?(2)] $\frac{1}{\sqrt{2}}$ [1s(1)2s(2)?1s(2)2s(1)]?(1)?(2)

          2. Use slater determinants to show that the 1st excited state of Helium atom can be
expressed as below.
$\frac{1}{2}$ [1s(1)2s(2)+1s(2)2s(1)][?(1)?(2)??(1)?(2)]
$\frac{1}{\sqrt{2}}$ [1s(1)2s(2)?1s(2)2s(1)]?(1)?(2)
$\frac{1}{2}$ [1s(1)2s(2)?1s(2)2s(1)]?(1)?(2)][?(1)?(2)+?(1)?(2)]
$\frac{1}{\sqrt{2}}$ [1s(1)2s(2)?1s(2)2s(1)]?(1)?(2)

2. Use slater determinants to show that the 1st excited state of Helium atom can be
expressed as below.
(1)/(2) [1s(1)2s(2)+1s(2)2s(1)][?(1)?(2)??(1)?(2)]
(1)/(√(2)) [1s(1)2s(2)?1s(2)2s(1)]?(1)?(2)
(1)/(2) [1s(1)2s(2)?1s(2)2s(1)]?(1)?(2)][?(1)?(2)+?(1)?(2)]
(1)/(√(2)) [1s(1)2s(2)?1s(2)2s(1)]?(1)?(2)

Added by Thomas P.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sachin Rao

Step 1

First, let's define the Slater determinant for the 1s and 2s orbitals of the Helium atom: Ψ(1s(1)2s(2)) = (1/√2) [1s(1)2s(2) - 1s(2)2s(1)] Show more…

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Use Slater determinants to show that the 1st excited state of the Helium atom can be expressed as below: [1s(1)2s(2) + 1s(2)2s(1)][a(1)(2) - a(2)] [1s(1)2s(2) - 1s(2)2s(1)]a(1)a(2) [1s(1)2s(2) - 1s(2)2s(1)]a(1)a(2)][a(1)(2) + a(2)] [1s(1)2s(2) - 1s(2)2s(1)](1)(2) / 2