3. A hydrogen atom is in a superposition of stationary states described by the state vector: -Ey -E A A Y(F₁1) = 100€ "

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3 A Hydrogen Atom Is In A Superposition Of Stationary States Described By The State Vector Ey E A A Y F 1 100 1 (44.23 KiB) Viewed 13 times

3. A hydrogen atom is in a superposition of stationary states described by the state vector: -Ey -E A A Y(F₁1) = 100€ " + + 4/300€ +(2520 +10 ++4322) e C = is the energy eigenfuction belonging to the energy eigenvalue E, 2 where a. Which of the following operators share eigenfunctions for the hydrogen atom and why? n' H.L,L,,L,,L.,P. b. Which of the following can not describe a stationary state of hydrogen? (Identify those with impossible quantum numbers, and describe the incompatibility): 311 V123 W321 V 402, and 21-1 c. For the state specified by Y(F,1) above, what is the probability of obtaining E = Es upon measurement? What is the probability of obtaining E = E, and E E3? d. For the state specified by Y(F,) above, what is the probability that a measurement of L² will yield 6ħ² and what is the probability that a measurement of L. will yield 0ħ? e. Calculate the expectation values of E. L²,L..