1. Operators for the properties B and C, give the following results when applied to a set of orthonormal functions, X. Note: bj, cj, ẞi, and Yi are all constants in this problem. BXk = bk-1Xk-1 Ĉ Xk = Ck+1 xk+1 a) What is the value of BC X4 ? Show your work explicitly. * b) What is the value of XC² X, dt? Show your work explicitly. as c) Do the operators B and Ĉ commute? Show your work explicitly. d) Is there a set of functions, &;, such that Bi = = Bio; and Ĉi = Yii? Explain. 2. What is the value of (33) for the n 3 state of the 1D particle in a box of length a? Show your work and/or explain vour answer.