A one-dimensional harmonic oscillator is in a state |) = N[|1) - √√2|2) + 3i|3) − 2 |4)]| where the kets on the right are the oscillator eigenkets |n) with quantum number ʼn . (a) What is the probability that the system is in the first excited state? (b) What is the average energy of the system? (c) What is the expectation value of the system's potential energy? (d) What is the average position of the system?

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