Quantum Engi Q and A_Part_18

Quantum Engi Q and A_Part_18 - 52 4.4 CHAPTER 4....

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52 CHAPTER 4. SINGLE-PARTICLE SYSTEMS 4.4 The Commutator 4.4.1 Commuting operators 4.4.1.1 Solution commutea-a Question: The pointer state 2p x = 1 2 ( ψ 211 + ψ 21 1 ) . is one of the eigenstates that H , h L 2 , and h L x have in common. Check that it is not an eigenstate that H , h L 2 , and h L z have in common. Answer: It is an eigenstate of H and h L 2 , but not of h L z . Since the z -angular momentum of a ψ nlm state is m ¯ h , the combination above has a 50%/50% probability that the z -angular momentum is ¯ h or ¯ h . 4.4.2 Noncommuting operators and their commutator 4.4.3 The Heisenberg uncertainty relationship 4.4.3.1 Solution commutec-a Question: This sounds serious! If I am driving my car, the police requires me to know my speed (linear momentum). Also, I would like to know where I am. But neither is possible according to quantum mechanics.
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4.5. THE HYDROGEN MOLECULAR ION 53 Answer: On second thought, maybe I can relax. According to the uncertainty relationship, the uncertainties could be as small as, for example,
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Quantum Engi Q and A_Part_18 - 52 4.4 CHAPTER 4....

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