IN der V three parts into the right-hand side of (8.106), and ar /ad = 0. (e) Sub ge121-H Use sepa- es and seek a silution of the form Netabig a =b=c ahal her af Emple 82 unhers , are any show that you get the left-hand side. SECTION 8.5 (The Three-Dimensional Central- Force Problem) woOimensional Central- 8.20 .The spherical polar coordinates (r, 0, 6) are de- fined in Fig. 8.11. Derive the expressions given there for x, y, and z in terms of (r, 0, ). Find corresponding expressions for r, 0, and in terms of (x, y, z). polar coordinates Secn pve the relations m yrm B104 gp for r and d in 8.21A point P on the earth's surface has rectangular coordinates (x, y, z) and spherical polar coordinates (r,0,6) (with coordinates defined so that the origin is at the earth's center and thez axis points north What are the coordinates (rectangular and spherical winnin as rectangular alie ines r What d pit -1-y apde insmenins(such as of the place Q at the oppositn ter through tR iome 264 Chapter 8 The Three- Dimensional Schrödinger Equation good cause, namely, the understanding of twentieth-century science. Since the potential energy of any particle's distance from the force center tem that includes r as one of the coordina P(x, y, z) or (r, 0, ) Z=r cos e у cOordinates, which are defined in Fig. 8.1 three coordinates (r, 0, ), where r is the between the z axis and OP, and is the vertical plane containing OP, as shown.* earth's surface and put the origin O at the ing to the north pole, then 0 is the colatitud from the north pole) and is its longitud from the x-z plane. The angle 0 lies betwe south pole. If increases from 0 to 2T (w earth at fixed latitude and returns to its sta X=r sin cos y = r sin 0 sin х FIGURE 8.11 The spherical polar coordinates of a point P are (r, 0, d), where r is the distance OP, 0 is the angle between OP and the z axis, and is the angle between the x-Z plane and the vertical plane containing OP. nates (x, y, z) are given in terms of (r, 0, d