The state of an electron in a hydrogenic atom is given by the un-normalized wavefunction $$\Phi = \left\{ Y_{10}(\theta, \phi) + \frac{1}{\sqrt{2}} Y_{11}(\theta, \phi) \right\} R(r)$$ $$\text{where } Y_{l m}(\theta, \phi)$$ are spherical harmonics and R(r) is the radial function. The probability that a measurement of L_z will give an eigenvalue of ℏ is

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Correct option is C

The angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role in the theory of atomic and molecular physics and other quantum problems involving rotational symmetry. Being an observable, its eigenfunctions represent the distinguishable physical states of a system's angular momentum, and the corresponding eigenvalues the observable experimental values. When applied to a mathematical representation of the state of a system, yields the same state multiplied by its angular momentum value if the state is an eigenstate (as per the eigenstates/eigenvalues equation).