Quick Quantum Eigenstate Question

  • Thread starter matt223
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Homework Statement



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

All states are normalised and:

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

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

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 [tex]\left | \mu_1 \right \rangle[/tex]. Thank you for any help!
 
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Answers and Replies

  • #2
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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 [tex]<\mu_1|\hat L|\mu_1>[/tex] be? What about [tex]<\mu_0|\hat L|\mu_1>[/tex]? Is it possible to calculate the energy of the angular momentum states: [tex]<\mu_1|\hat H|\mu_1>[/tex]?
 

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