p=mv, a three-dimensional Cartesian vector y-component of angular momentum: Ly=ZPx-Xpz 3. Transform the following operators into the specified coordinates h a Lx=11yaz-z8y1 from Cartesian to spherical polar coordinates i ao from spherical polar to Cartesian coordinates 4. Match the eigenfunctions in column B to their operators in column A. What is the eigenvalue for each eigenfunction? Column A Column B d2 d Ix2-x dx 4x4-12x2+3 lll7 p = mv, a three-dimensional Cartesian vector. y-component of angular momentum: Ly = zpx - xpz. 3. Transform the following operators into the specified coordinates: Lx = -h i îï í ïì þï ý ïü y ¶ ¶z - z ¶ ¶y from Cartesian to spherical polar coordinates. Lz = h - i ¶ ¶f from spherical polar to Cartesian coordinates. 4. Match the eigenfunctions in column B to their operators in column A. What is the eigenvalue for each eigenfunction? Column A Column B i. (1-x2) d2 dx2 - x d dx 4x4 - 12x2 + 3 ii. d2 dx2 5x4 iii. x d dx e 3x + e-3x