An electron in a hydrogen atom is in a state described by the wave function: ?(r

Question

An electron in a hydrogen atom is in a state described by the wave function:

?(r,?,?)=R(r)[cos(?)+ei?(1+cos(?))]

What is the probability that measurement of L2will give 6?2and measurement of Lzwill give ? I know that I need to express the part in (?,?) as a linear combination of spherical harmonics. Then I would normalize my wave function, and the coefficients would lead me to the probability I need.

My problem is to express ? in terms of the spherical harmonics Ylm. Is there a general method to do so? Thanks. An electron in a hydrogen atom is in a state described by the wave function:

?(r,?,?)=R(r)[cos(?)+ei?(1+cos(?))]

What is the probability that measurement of L2will give 6?2and measurement of Lzwill give ? I know that I need to express the part in (?,?) as a linear combination of spherical harmonics. Then I would normalize my wave function, and the coefficients would lead me to the probability I need.

My problem is to express ? in terms of the spherical harmonics Ylm. Is there a general method to do so? Thanks. An electron in a hydrogen atom is in a state described by the wave function:

?(r,?,?)=R(r)[cos(?)+ei?(1+cos(?))]

What is the probability that measurement of L2will give 6?2and measurement of Lzwill give ?

Explanation / Answer

An electron in a hydrogen atom is in a state described by the wave function: ?(r,?,f)=R(r)[cos(?)+eif(1+cos(?))] You could find the projection of the angular part onto the state |l m? by calculating ?l m|??. Seems to be kind of a pain though. I'd just futz around with the spherical harmonics to find a linear combination that works. For example, the ei? part has to come from an m=1 state.

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