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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?

Can you please show me a step by step solution for how to solve these type of questions.

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The solution shows in detail how to get the possible values of an obesrvable and the measuremant probabilities using the linear combination representation.

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Let the basis of the system be represented by a set of orthonormal eigenfunctions
Since this functions are orthonormal they satisfy:
(1.1)
We can write any wavefunction as a linear combination of the eigefunctions:
(1.2)
The probability to find the system is state is the modulus-square of the projection of on ...

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