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.
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Transcribed Image Text: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:
7.
4
Y(x, y,z)=.
n,Ty
sin
sin
2a
sin
a
The Hamiltonian operator is:
Ĥ = -
2m Ox
a) 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 of
triply-degenerate energy levels.
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