Quiz1solution - Name: - - Student 10: - Quiz #1 (Closed...

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--------- ------- Name: Student 10: Quiz #1 (Closed book. Calculator and one infonnation sheet allowed; written on both sides o.k.) Physics 113B Quantum Mechanics Monday, October 18,2010 1. (7 points) For three identical particles, write down the properly nonnalized symmetric antisymmetric states for the spatial wavefunctions. Assuming the three particles are in different spatial states \Va, \Vf3' \Vy with quantum numbers (1, 13, and y. 'SimM-t~-'-- S+NtL :. ~< ( I J L ~) ~ -L [. 1" (,) 't'. l'z. .) \i. ., (s) ... 'fA (.) \f ("L) 'f~ (~) j I ~ '17:' 1;J. . p I flY + 1ft) t(/ (,) 'f-! (~) -t 'fl) '1/.) ~ (~) ~ 'If (I) 't. .(~) 'f- y + ~ fit) '1/ 3 )'1 (h. .j; s r-. M " stdL : t(l) lfll-t"l-) If (~) (Jl. 'f p 'f p (,) f/> (s) \.f l i l ) t y (~) t. (1,) t to'if (I, t) 3) = if l ~ ~ ("t.) If ~/!» t ~ ~ (t) ~ /1) A () 'f{)'!l2.)y.-(~) + ¥ (f) ~ I t.) 'ft 3 - ( I f (.. 1 _ Y- 'f ("l.) ~ (;) - y;;. bl 'Iio.-) f (3) r ol 1
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2. (4 points) Pion 1t- is a spin-O particle ~280 times more massive than the electron. Suppose the two electrons in a helium atom are replaced by two negative charged pions, forming a pionic atom. Write down the wave functions for (a) the ground state, and (b) the first excited state for pionic helium. 3. (2 points) Write down the ground state wave function for the helium atom? Provide explicitly both the spatial and spin
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Quiz1solution - Name: - - Student 10: - Quiz #1 (Closed...

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