= mw2,2 2 Consider now a 3D spherically-symmetric harmonic oscillator potential, V(r) (a) Using the factorization of the

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Mw2 2 2 Consider Now A 3d Spherically Symmetric Harmonic Oscillator Potential V R A Using The Factorization Of The 1 (65.71 KiB) Viewed 21 times

= mw2,2 2 Consider now a 3D spherically-symmetric harmonic oscillator potential, V(r) (a) Using the factorization of the wave-function into the X-, Y-, and Z- components, calculate the energies of the ground state and the first excited state. Write down explicitly the ground state wave-function, 4000(r), and show that it is in fact spherically symmetric. (b) What is the degeneracy of the first and second excited states? (c) Use the spherical symmetry to write down the radial Schödinger equation in an effective potential the harmonic oscillator potential and the centrifugal potential parameterized by the angular variable, 1 (see lectures and the texbook). (d) Explicitly verify that the ground state wave-function, found earlier, satisfies the corresponding radial Schrödinger equation.