Quick Quantum Eigenstate Question

matt223
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Homework Statement



An atomic system has 2 alternative 2-state bases. The angular momentum bases are \left | \mu_i \right \rangle with L_0 = 0 and L_1 = 1. The energy eigenstates are \left | \phi_i \right \rangle with E_0 and E_1.

All states are normalised and:

\left | \mu_0 \right \rangle = \frac{1}{2} \left | \phi_0 \right \rangle + \frac{\sqrt 3}{2} \left | \phi_1 \right \rangle

Write down an expression for \left | \phi_1 \right \rangle in terms of \left | \mu_i \right \rangle.

Homework Equations



The Attempt at a Solution



This should be straight forward however I cannot see how this can be done without an equation for \left | \mu_1 \right \rangle. Thank you for any help!
 
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You may want to consider some of the basic properties of these quantum states. For example, what must the value of <\mu_1|\hat L|\mu_1> be? What about <\mu_0|\hat L|\mu_1>? Is it possible to calculate the energy of the angular momentum states: <\mu_1|\hat H|\mu_1>?
 

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