Consequences of Wave Mechanics:

1.

Electron Interference Pattern

2.

Uncertainty Principle

$$\triangle x\triangle p\geq\frac{h}{2\pi }$$ (35)

3.

Particle in a Box:

$$\psi_n(x) = A\sin\left(\frac{n\pi x}{L}\right)$$ (36)

(fundamental modes)      n = 1,2,3,...

$$P_n = \frac{h}{\lambda_n} = \frac{nh}{2L}$$ (37)

$$E_n = \frac{P^2_n}{2m} = \frac{n^2h^2}{8mL^2}$$ (38)

4.

Hydrogen Atom:

mv_nr_n = nh (39)

r_n = a_on² (40)

$$E_n = -\frac{ke^2}{2a_o}\frac{1}{n^2}$$ (41)