1What is the physical significance of normalizing a wave function Ψ?
2
According to the course material, what is the ground state energy (n=1) for an electron in a 1D box of length 0.2 nm? (Use h = 6.626e-34 J s and m = 9.109e-31 kg)
3For an operator Ô and a function f(x), if Ôf(x) = k f(x), what is k called?
4The Born-Oppenheimer approximation is primarily used to:
5Calculate the ionization energy of Li²⁺ in its ground state using the formula En = -13.60 (Z²/n²) eV.
6Which of the following statements are true regarding a particle in a 3D rectangular box with sides Lx, Ly, and Lz?
7If the operator B̂ has the property B̂² = B̂, what are the only possible eigenvalues for the equation B̂Ψ = bΨ?
8Identify the boundary conditions applied to a particle in a 1D box of length L (from x=0 to x=L).
9What is the eigenvalue when the momentum operator p̂x = -iħ(d/dx) is applied to the function Ψ = e^(ikx)?
10Given the function Ψ = Ax(1-x) in the interval 0 ≤ x ≤ 1, what is the normalization constant A?
