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4. 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. Visa (ri) 1sẞ(1) 280 (1) 1 V(r1, r2, r3): = Visa (r2) 1sẞ(r2) V2sa(r2) √6 Visa (3) 1sẞ(r3) 428α(3) 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.

4. 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. Visa (ri) 1sẞ(1) 280 (1) 1 V(r1, r2, r3): = Visa (r2) 1sẞ(r2) V2sa(r2) √6 Visa (3) 1sẞ(r3) 428α(3) 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
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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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4. 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. Visa (ri) 1sẞ(1) 280 (1) 1 V(r1, r2, r3): = Visa (r2) 1sẞ(r2) V2sa(r2) √6 Visa (3) 1sẞ(r3) 428α(3) 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.
Transcribed Image Text:4. 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. Visa (ri) 1sẞ(1) 280 (1) 1 V(r1, r2, r3): = Visa (r2) 1sẞ(r2) V2sa(r2) √6 Visa (3) 1sẞ(r3) 428α(3) 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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