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Sharp values of wavefunction in polar coordinates

  • Thread starter ParoxysmX
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  • #1
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Homework Statement


Consider the function in polar coordinates

ψ(r,θ,[itex]\phi[/itex]) = R(r)sinθ[itex]e^{i\phi}[/itex]

Show by direct calculation that ψ returns sharp values of the magnitude and z-component of the orbital angular momentum for any radial function R(r). What are these sharp values?

The Attempt at a Solution



I -think- for [itex]L_{z}[/itex] to be sharp, you have to impose the eigenfunction condition

[itex]-i\hbar \frac{dψ}{d\phi} = L_{z}ψ[/itex]

which means that the radial function R(r) would cancel with itself if you were to rearrange the above for [itex]L_{z}[/itex]. However I could have completely the wrong idea here.
 

Answers and Replies

  • #2
DrClaude
Mentor
7,281
3,442
How about calculating the expectation values corresponding to "the magnitude and z-component of the orbital angular momentum "?
 

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