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Unformatted text preview: H = =&lt;T&gt; + &lt;V&gt; (from above): Physics 486 Fall 2007 2). Consider a particle in an isotropic 3D harmonic oscillator potential, V(x,y,z) = m 2 x 2 + m 2 y 2 + m 2 z 2 . (a). Write the energy eigenvalues for a particle confined to this potential in terms of the angular frequency and the quantum numbers n x , n y , and n z . (b). Write, in the table below: (i) the total energy, (ii) the states (n x ,n y ,n z ) associated with each total energy, and (iii) the degeneracy g n (where n=n x +n y +n z ) associated with each total energy, for the lowest 4 energies of the 3D harmonic oscillator. n=n x +n y +n z 0 1 2 3 E n (n x , n y , n z ) g n...
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