A 3-D particle in a box has dimensions of x = 0 to a, y = 0 to a, and z = 0 to 2a. The normalizedWavefunction is:7.4Y(x, y,z)=.n,Tysinsin2asinaThe Hamiltonian operator is:Ĥ = -2m Oxa) Apply A to Y and find E,b) Show that the sets of quantum numbers(n, ny, nz) = (1,2,2), (2,1,2), and (1,1,4) represent a set oftriply-degenerate energy levels.

we know the formula that Given A 3 d particle in a box has dimensions of x = 0 to a…

A 3-D particle in a box has dimensions of x = 0 to a, y = 0 to a, and z = 0 to 2a. The normalized Wavefunction is: 4 sin n,Ty ·sin n.TZ sin 2a a The Hamiltonian operator is: h (a Ĥ = 2m ôx a) Apply A to Y and find E, m. b) Show that the sets of quantum numbers(n, ny, n2) = (1,2,2), (2,1,2), and (1,1,4) represent a set of triply-degenerate energy levels.

A 3-D particle in a box has dimensions of x = 0 to a, y = 0 to a, and z = 0 to 2a. The normalized Wavefunction is: 4 sin n,Ty ·sin n.TZ sin 2a a The Hamiltonian operator is: h (a Ĥ = 2m ôx a) Apply A to Y and find E, m. b) Show that the sets of quantum numbers(n, ny, n2) = (1,2,2), (2,1,2), and (1,1,4) represent a set of triply-degenerate energy levels.