Solve the TISE (time-independent Schrödinger equation) for each of the potentials 1 to 7.
1.
V(x) = { (0, if x < 0), (V₀ if x ≥ 0) }
V(x) = { (0, if x < 0), (V₀ if 0 ≤ x ≤ a), (0, if x > a) }
V(x) = { (+∞, if x < -(a/2)), (V₀ if (a/2) ≤ x ≤ (a/2)), (+∞, if x > (a/2)) }
V(x) = { (V₀, if x < -(a/2)), (0 if -(a/2) ≤ x ≤ (a/2)), (V₀, if x > -(a/2)) }
V(x) = (1/2) mω²x²
V(x) = { (-∫₋∞)^(∞) V(r)δ(r - r₀)dr if 0 ≤ r ≤ r₀), (0 if r > r₀) }
V(x) = (ħ²γ) / (2) δ(x)
In each case, find the energies and wave functions of the bound states, make plots of the wave functions, and give the physical interpretation of the solution in each case. Verify the Heisenberg uncertainty principle in each case.
Solve the TISE (time-independent Schrödinger equation) for each of the potentials 1 to 7.
1.
Jo, if x < 0, V = V if x₀
2.
0, if x < 0,
V(x) = (V if 0 ≤ x ≤ a, (0, if x > a,
3.
(+∞ if x < - V() = (V₀ if x² (+∞, if x >
4.
(V₀ if x < -, V) = 0 if -x V₀ if x > -
5.
1
(1)
6.
l0 if r > r₀
7.
V() = hY8(e) 2
(2)
In each case, find the energies and wave functions of the bound states, make plots of the wave functions, and give the physical interpretation of the solution in each case. Verify the Heisenberg uncertainty principle in each case.