(a) Explain whether this system is symmetric or not for the given operation below.

-rotation

(b) When the eigenstate of this system is lnx ny nz>, try to matrix representation of the position operator r=xi+yj+zk based on all the eigenstates corresponding to the two lowest energy eigenvalues. At this time, consider that the parity selection rule and the eigenvectors for each component are orthonormal, first find the matrix elements that become 0, and calculate only the non-zero matrix elements.

are particles with mass m are affected by the following three-dimensional harmonic oscillator potential, oscillating at the same frequency w in all directions. V(x, y, z) = mw(x+4 +2) 2% +2 Dryer) + mwam? Hor) = Eur) de todo en todos tumore = xe my chanz, ) &mwh pa ma? (x + y 24 23 ) Eneng nz = Era + Eng + Eng = (x+4) kwa +(1672) twy +(12 t1)t wa -> de mw x = Eve You (x) I'm Y Cb) + Iow, y=E, Y.CD) h 22 in de Zn_(7) + 'm wo de mw x = Eve You (x) I'm Y Cb) + Iow, y=E, Y.CD) h 22 in de Zn_(7) + 'm wo