Which of the following statements is true? A.The total energy eigenfunctions for

Question

Which of the following statements is true?

A.The total energy eigenfunctions for rotation in three dimensions can be written in the form Y(, ) = ()() because the potential energy is independent of the angles and .

B.Two quantum numbers are needed to characterize the eigenfunctions for rotation in two dimensions, whereas three quantum numbers are needed to characterize the eigenfunctions for rotation in three dimensions.

C.Because the operators Equation, , and Equation commute, the z-axis describes a preferred direction in space.

D.The angular momentum vector for 3-D rotation has three components.

1. A and B 2. A and D 3. B and D 4. B and C

Explanation / Answer

Which of the following statements is true?

A.The total energy eigenfunctions for rotation in three dimensions can be written in the form Y(, ) = ()() because the potential energy is independent of the angles and .------------answer

B.Two quantum numbers are needed to characterize the eigenfunctions for rotation in two dimensions, whereas three quantum numbers are needed to characterize the eigenfunctions for rotation in three dimensions.-wrong

C.Because the operators Equation, , and Equation commute, the z-axis describes a preferred direction in space.

D.The angular momentum vector for 3-D rotation has three components.

1. A and B

2. A and D ---------answer

3. B and D

4. B and C

For rotation in two dimensions, the angular momentum vector has only one component, and the vector is perpendicular to the plane of rotation.

For rotation in three dimensions, the angular momentum vector has three components.

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