| 3.2 |
Operators for K.E and  |
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(b) |
Fig 3.2: a) Plane polar coordinate system, r,
 in the x y plane (two dimensions) and b) Spherical coordinate system r, , (three dimensions). |
| In two dimensions, the kinetic energy is p x 2 / 2m + p y 2 / 2m. We are assuming that the motion is in the x,y plane.
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The operator for px is (  / i )  / x and that for px 2 is – 2 2 /x 2 (lecture 2). The operator for K.E is.......... . - 2 / 2m ( 2 /x 2 + 2 /y 2 ). In spherical polar coordinates wherein the variables are r, , in place of xyz (in 3 dimensions). In a plane, the polar coordinates are r and (in two dimensions) in place of x and y and it is possible to show that in two dimensions, we obtain the following forms for the operators for energy and angular momentum. |
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