Question

The Pauli Exclusion Principle In this problem we will try to see how the requirement that the multi-electron wave function be antisymmetric under the exchange of two particles is related to the more familiar “Pauli exclusion principle”. Consider two non-interacting spin-particles in a 1D box of length 1, with the two particles in the excited configuration: V - 1012(x1) 02a(x1)| Y = € 1010(x2) 02a(2) | Take 01 = V2 sin(1x) and $2 = V2 sin(2tex). a) Verify that Ye satisfies the time independent Schrödinger equation. b) Make a 2-dimensional plot of Ye(x1, x2)12. What happens when x1 = x2? Interpret your results in the context of the Pauli exclusion principle

Answer 1

Ans: Given that Wave function as determinantis Year Celta (2) pie (Be) - - Pra (2.) praci fare Ø :12 Sin (Tix) ; , -T2 Sin (2714) 0 = 82 T (os (TTX); $2 = -√2 Asin (TX) = -13 / 2 x = -452T? Sin&tx) = -477²42

a) time Independent Shrodinger egn. i e. We should get R. His = aconstant 4 dus - 541 (2) 6.(x)+23%. (: -|(2) 6 (3.)-8 (60)] Putting allwalues weget e Ti²q + Constant 4 a A A A A A A Probability T o v Halong x series x = X₂ Therefor Ston The wave function vanished for the probability becomes Zero N