4. Consider an operator  satisfying the commutation relation [Â, †] = 1. (a) Evaluate the commutators [†Â, Â] and [†‚ †]. Let a be a state vector satisfying the inner product (a'|a) actions of  and Ât on a state vector |a) are given by = Sa'a Suppose that the (b). Â|a) = √ala – 1), †|a) = √√a +1|a +1). Calculate the inner products (a|†Â|a), and (a¦Â†|a). (c) Calculate (a|( + †)²|a) and (a[( — †)²|a).
4. Consider an operator  satisfying the commutation relation [Â, †] = 1. (a) Evaluate the commutators [†Â, Â] and [†‚ †]. Let a be a state vector satisfying the inner product (a'|a) actions of  and Ât on a state vector |a) are given by = Sa'a Suppose that the (b). Â|a) = √ala – 1), †|a) = √√a +1|a +1). Calculate the inner products (a|†Â|a), and (a¦Â†|a). (c) Calculate (a|( + †)²|a) and (a[( — †)²|a).
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![4. Consider an operator  satisfying the commutation relation [Â, †] = 1.
(a)
Evaluate the commutators [†Â, Â] and [†‚ †].
Let a be a state vector satisfying the inner product (a'|a)
actions of  and Ât on a state vector |a) are given by
= Sa'a Suppose that the
(b).
Â|a) = √ala – 1), †|a) = √√a +1|a +1).
Calculate the inner products (a|†Â|a), and (a¦Â†|a).
(c)
Calculate (a|( + †)²|a) and (a[( — †)²|a).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F307e7dc6-5ee6-49a3-8b7c-3843abe12d11%2F54477217-7e56-49f3-8c72-9569739e25ed%2Fhy4532x_processed.png&w=3840&q=75)
Transcribed Image Text:4. Consider an operator  satisfying the commutation relation [Â, †] = 1.
(a)
Evaluate the commutators [†Â, Â] and [†‚ †].
Let a be a state vector satisfying the inner product (a'|a)
actions of  and Ât on a state vector |a) are given by
= Sa'a Suppose that the
(b).
Â|a) = √ala – 1), †|a) = √√a +1|a +1).
Calculate the inner products (a|†Â|a), and (a¦Â†|a).
(c)
Calculate (a|( + †)²|a) and (a[( — †)²|a).
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