4.2 Let T₁ denote the translation operator (displacement vector d); let D(n,d) denote the rotation operator (n and are the axis and angle of rotation, respectively); and let denote the parity operator. Which, if any, of the following pairs commute? Why? (a) Ta and T (d and d' in different directions). (b) D(n,) and D(',') (f and f' in different directions). (c) T₁ and 7. (d) D(n,) and .
4.2 Let T₁ denote the translation operator (displacement vector d); let D(n,d) denote the rotation operator (n and are the axis and angle of rotation, respectively); and let denote the parity operator. Which, if any, of the following pairs commute? Why? (a) Ta and T (d and d' in different directions). (b) D(n,) and D(',') (f and f' in different directions). (c) T₁ and 7. (d) D(n,) and .
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Transcribed Image Text:42 Let Ta denote the translation operator (displacement vector d); let D(n,p) denote
the rotation operator ( and are the axis and angle of rotation, respectively); and
let denote the parity operator. Which, if any, of the following pairs commute?
Why?
(a) Ta and T (d and d' in different directions).
(b) D(n,p) and D(n, ') (ñ and f' in different directions).
(c) T₁ and .
(d) D(n,) and .
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