Quantum Mechanics Practice Problems Solutions - Free Printable

1.
- Âf(x) = 2x e^(-x²/2)
- B̂f(x) = 0

2.
a. k → eigenfunction with eigenvalue 0
b. kx² → not an eigenfunction
c. sin(kx) → not an eigenfunction
d. e^(kx) → eigenfunction with eigenvalue k
e. e^(kx²) → not an eigenfunction
f. e^(ikx) → eigenfunction with eigenvalue ik

3.
a. [x̂, p̂_x] = iħ
b. [x̂, p̂_x²] = 2iħ p̂_x
c. [x̂, p̂_y] = 0

4.
L̂_x = -iħ (y ∂/∂z - z ∂/∂y)