Question

A linear combination of two wave functions for a system is also a valid wave function. Find the normalization constant for the combination ψ = B(sin nπx L + sin πx L ) of the wave functions for the n = 1 and n = 2 states of a particle in a box L wide

Answer 1

$\psi=B(\sin\frac{n\pi x}L+\sin \frac{\pi x}L),$

$\int_0^L\psi^2dx=1,$

$n=1:$

$B=\sqrt\frac 1L,$

$n=2:$

$B=\sqrt\frac 1L.$