Question

Problem 2 Consider a particle on a sphere of fixed radius r and V = 0 on the spherical surface. The particle is found in either of the following wavefunctions: Y1,1(0,0) or Y1,-1(0,0). a) What is the energy difference between the two possible wavefunctions? b) Determine the magnitude of angular momentum and its projection onto the z-axis for both wavefunctions. c) Do the energy and the magnitude of angular momentum change when the radius r of the sphere is increased? d) The functional form of the wavefunctions are Y1,+1(0,0) = F(3)"sin Oetio. What is the probability of finding the particle at the following locations: {0,0} = {0,0} and {0,0} = {{1, 37}?

Answer 1

Rotational Energy, E = llo+1) h2 amrz Rajshree PAGE NO: DATE (6 state & Yomlu, d) Eo depend on bli Hence Energy will be game for Y Cod) & (0,d). So energy Difference will be zero 111 - 110 +1 +2 - 1 (1+1)+2 = 2t2 for yg & X 7- Componend z-mt = t for 71 6 © I = tw- moro L L 82 & ELI 82 AS & increases then E will decregue and 1 will increase 0 7 (0,0) = = 132 sino e la i ono o sino)

Rajshree PAGE NO.: DATE Probability for 7,110,0) PITX1200) X., 10,0) smo do df = 04 similarly for 7, (0, d) , P-og Po Mar 19, 10,097)? mimo do do = 1 st r ging de de sin (30) - 3 incu- 4613 YL 81138 -13 enco - 39(30) 1 få sin le do sa sino de-4f en tourdo --3, 6000 m + her cor/201122 JO 4x3 10 fatory 22 -0.6667 Sume - 97 P = 66.67% probability will be for - 66.67 7. s 8 (@, d)