Question: Please show all the work (II) Consider these operators: 0 =) = 02 = a a a + az a2 a a + a.x2 az

Please show all the work (II) Consider these operators: 0 =)

Please show all the work

(II) Consider these operators: 0 =) = 02 = a a a + az a2 a a + a.x2 az a2 a2 a2 ay2 " az2 - 03 ac? acting on these wave functions: V.(x, y, z) = A sin(kzx) sin(kyy) sin(kzz) 16(%, y, z) = Aeik-te-1(y2+z4 V.2, y, z) = A sin(k_c)e-1(ya+z2) = Assume that I ER and I >0. Act with each operator on each wavefunction and based on the result, decide if the given wavefunction represents an eigenstate of the operator? If so, what is the eigenvalue? Provide a detailed answer and show your reasoning mathematically

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