wave function (x, y, z) = A sin(kx) sin(k₂y) sin(kz) into - v² = E. 2m
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Transcribed Image Text:Complete the derivation of E =
Taking the derivatives we find (Use the following as necessary: k₁, K₂ K3, and 4.)
+- ( ²) (²)
v² =
SO
- #2² -
=
2m
so the Schrödinger equation becomes (Use the following as necessary: K₁, K₂, K3, ħ, m and p.)
亢
2mm(K² +K ² + K² v
k₁ =
E =
= EU
The quantum numbers n, are related to k, by (Use the following as necessary: n, and L₁.)
лħ n₂
π²h²
2m
√2m
h²²/0₁
2m
X
+
+
by substituting the wave function (x, y, z) = A sin(kx) sin(k₂y) sin(kz) into -
13³3).
X
What is the origin of the three quantum numbers?
O the Schrödinger equation
O the Pauli exclusion principle
O the uncertainty principle
Ⓒthe three boundary conditions
2² 7²4 = E4.
2m
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