An angular momentum system is prepared in the state
|Psi> = 1/Sqrt(10) ( |1 1> - 2|1 0> + 2i|2 2> + i |2 0>)
What are the possible results of a measurement of the squared angular momentum L_hat^2 and with what probabilities would the occur?
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The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.
Let the basis of the system be represented by a set of orthonormal eigenfunctions
Since this functions are orthonormal they satisfy:
We can write any wavefunction as a linear combination of the eigefunctions:
The probability to find the system is state is the modulus-square of the projection of on ...
The solution shows in detail how to get the possible values of an obesrvable and the measuremant probabilities using the linear combination representation.