Answered: 6.2. Solve the three-dimensional… | bartleby

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6.2. Solve the three-dimensional harmonic oscillator for
which
1
V(r) = -— mw² (x² + y²² +2²)
2
by separation of variables in Cartesian coordinates.
Assume that the one-dimensional oscillator has
eigenfunctions (x) with corresponding energy
eigenvalues En = (n + 1/2)hw. What is the degeneracy
of the first excited state of the oscillator?

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PROBLEM 2 Calculate the probability distribution of momenta p for a ld oscillator in the ground state (n = 0). Calculate the mean square dispersions (x2), (p²), and the product (r2)(p²).
1
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