Question

Exercise: In this exercise, you will calculate various expectation values for different wave functions corresponding to different potentials. These distributions appear in Table VIII. Table VIII Infinite Square Well 1-D Hydrogen Atom Finite Smooth Well (ground state) (ground state) A Wave Function Un(x) = A sin 4.(x) = A x exp Wo(x) = cosh(kx) SMHB hint 17.17.1 to 17.19.1 18.76, 25.3 U(x) = _ kee? Potential U(X) = 0 ħ2 12 n2 17.27.1 to 17.33.7, 25.3 U. U(x) = - cosh2(kx) h2 k2 mke' e4 Energy En = 2 m az En = - 2 h2 E = -2m Domain 0<x<a 0<x< -o0<x<00 h2 k2 Constraints n = 1,2,3, etc. AB=mk, ez Uom 1st Moment (Px) = (px) = (px) = 2nd Moment (Px2) = (p22) = (P22) = Apx = Apx = Apx = Standard Deviation Heisenberg Uncert. Princ. Ax Apx = Ax Apx = Ax Apx = Kinetic Energy (px) (Px2) 2m 2m 2m Potential Energy (U(x)) = (U(x)) = (U(x))= Total Energy (E) = (E) = (b) =

Answer 1

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sin <>- 10 Min) The Molay on - Samm) un sin moun ) an 24 may sin (maks) to mary 5 2 sin ( 1TM) da som fo- cas (ES)) da 6 2ntin ГОТІ ART <H) - <HT! fuego - mouth To find an <aya 2 ( a sin" (na) an 21 2012 a la salona), do -[ Je_cos Jan Jak malay on antigo) V. - + fia de ce SI DO i parlin w anan) da Zan 2 7 cu 2n - mar sin ennen les ta sin mo 28 (1) -Sin ant 2nri 2 na 2no

ZNAN - LOT (**)manas) dan Daca) (co anna) dx a la de la un cos ( 219 ) dx. 2 nn Co ni 2 /nnn 2nd 2x O, Inn 7) 2nti 2 non 17 TI O 2 non - 2 a z na 27 112noa nn ht nat - 2 min) = nith ( to me that 7m zm (un) - o <E> - <ula)) + 2M

40 km) - Anexp(-x) Un Vee kee Nowadang ini * est la ) dx Domainin ocneo 27 22 22 3 -1 2.100 Serat - 11 ( 1 et 31 dp = 7 (9) Fle) = => 14132 CHS (**) an a e a e е Now, 21 22

***/** а . + 2 + am 1) (b) a ta ao at 7 To find an (x) = lal 2% da = IAN (0) Pret de <*") - LAIN PYA da 12 • 24 sx -com, A S308-ad IN as

sa dan 2m 2m <U(*)> ankee (1/2) ket" de 29[*]. 1 zuta) = - he e ao KE) = <ula)> + KDV CRY - Kere end end

sa dan 2m 2m <U(*)> ankee (1/2) ket" de 29[*]. 1 zuta) = - he e ao KE) = <ula)> + KDV CRY - Kere end end