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Using the fact that the radial momentum operator is given by pr = -ihr, calculate the commutator [, pr] between the position operator, î, and the radial momentum operator.

Using the fact that the radial momentum operator is given by pr = -ihr, calculate the commutator [, pr] between the position operator, î, and the radial momentum operator.

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Please help with EXERCISE 6.21

Exercise 6.20 The wave function of a hydrogen-like atom at time t = 0 is 1 [√3y2,1,-1(7) — 42,1,0(7) + √5y2,1,1(7) + √2y3,1,167)], where nlm (r) is a normalized eigenfunction (i.e., nlm(†) = Rn1(r) Ylm (0, q)). (a) What is the time-dependent wave function? (b) If a measurement of energy is made, what values could be found and with what proba- bilities? (c) What is the probability for a measurement of ο which yields - 1ħ? Y (7,0) = Exercise 6.21 Using the fact that the radial momentum operator is given by pr = - iħr, calculate the commutator [f, pr] between the position operator, î, and the radial momentum operator. Exercise 6.22 Calculate Ar Apr with respect to the state
Transcribed Image Text:Exercise 6.20 The wave function of a hydrogen-like atom at time t = 0 is 1 [√3y2,1,-1(7) — 42,1,0(7) + √5y2,1,1(7) + √2y3,1,167)], where nlm (r) is a normalized eigenfunction (i.e., nlm(†) = Rn1(r) Ylm (0, q)). (a) What is the time-dependent wave function? (b) If a measurement of energy is made, what values could be found and with what proba- bilities? (c) What is the probability for a measurement of ο which yields - 1ħ? Y (7,0) = Exercise 6.21 Using the fact that the radial momentum operator is given by pr = - iħr, calculate the commutator [f, pr] between the position operator, î, and the radial momentum operator. Exercise 6.22 Calculate Ar Apr with respect to the state
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