The motion of a free particle on the surface of a sphere can be described using the Schrodinger equation A2 x/ = - 2IE 1 2 ) 4 , where 12 = 1 22 1 + sin 0 a sin2 0 262 sin 0 20 The solution of the above equation are the functions called spherical harmonics, Ye, me (0, 6), which satisfy the equation A2 Ye,me = - e(e+ 1) Ye, me, (1) where l = 0, 1, 2, ... me = l, e - 1 , ..., -e. The first few spherical harmonics are given below:e me Ye, me (0, $) 0 O VATT 0 3 V AT cos 0 +1 FV 8 7 sin getid Confirm that the spherical harmonic Y11 is a solution of Eq. (1). Remember that 0 and o are independent variables