The wavefunction of a particle is subjected to a sperically symmetric potential V (r) is given by (x) = (x + y + 3z)f(r), (1) where f is some function of the radius r alone. a) Is y an eigenfunction of L²? If so, what is its l-value? If not, what are the possible values of l we may obtain when L² is measured. b) What are the probabilities for the particle to be found in various m states? c) Suppose it is known that ý is an energy eigenfunction with energy eigenvalue E. Indicate how we may find V(r).
The wavefunction of a particle is subjected to a sperically symmetric potential V (r) is given by (x) = (x + y + 3z)f(r), (1) where f is some function of the radius r alone. a) Is y an eigenfunction of L²? If so, what is its l-value? If not, what are the possible values of l we may obtain when L² is measured. b) What are the probabilities for the particle to be found in various m states? c) Suppose it is known that ý is an energy eigenfunction with energy eigenvalue E. Indicate how we may find V(r).
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Transcribed Image Text:The wavefunction of a particle is subjected to a sperically symmetric potential V (r) is given by
(x) = (x + y + 3z)f(r),
(1)
where f is some function of the radius r alone.
a) Is y an eigenfunction of L²? If so, what is its l-value? If not, what are the possible values of l we
may obtain when L² is measured.
b) What are the probabilities for the particle to be found in various m states?
c) Suppose it is known that ý is an energy eigenfunction with energy eigenvalue E. Indicate how we
may find V(r).
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