Show that the Li atom wavefunction given by the following Slater Determinant is antisym- metric (i.e. the wavefunction changes sign) with respect to interchange of electrons at r₁ and r3. 1 V(r1, r2, r3) == √6 Visa (ri) isẞ(r1) Visa (r2) Visẞ(r2) 2sa (r2) Visa (3) 1sẞ(r3) 42,α(3) 2sa (1) Hint: Just expand out the determinant (see Math Chapter F for help), and then see what hap- pens if you swap the labels r₁ and r3. Note: It's antisymmetric with respect to interchange of any two electrons, and we just picked electrons 1 and 3 as an example.
Show that the Li atom wavefunction given by the following Slater Determinant is antisym- metric (i.e. the wavefunction changes sign) with respect to interchange of electrons at r₁ and r3. 1 V(r1, r2, r3) == √6 Visa (ri) isẞ(r1) Visa (r2) Visẞ(r2) 2sa (r2) Visa (3) 1sẞ(r3) 42,α(3) 2sa (1) Hint: Just expand out the determinant (see Math Chapter F for help), and then see what hap- pens if you swap the labels r₁ and r3. Note: It's antisymmetric with respect to interchange of any two electrons, and we just picked electrons 1 and 3 as an example.
Chemistry
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Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Transcribed Image Text:Show that the Li atom wavefunction given by the following Slater Determinant is antisym-
metric (i.e. the wavefunction changes sign) with respect to interchange of electrons at r₁ and
r3.
1
V(r1, r2, r3)
==
√6
Visa (ri) isẞ(r1)
Visa (r2) Visẞ(r2) 2sa (r2)
Visa (3) 1sẞ(r3) 42,α(3)
2sa (1)
Hint: Just expand out the determinant (see Math Chapter F for help), and then see what hap-
pens if you swap the labels r₁ and r3. Note: It's antisymmetric with respect to interchange
of any two electrons, and we just picked electrons 1 and 3 as an example.
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