Question

Problem 7-3. Show that the wave function ψ given by Eq. (7-6) satisfies the boundary conditions given by Eq. (7-5) if the values of k_x, k_y, and k_z are restricted to those of Eq. (7-7).

Eq. ( 7- 5 ) : ψ( x + L , y, z,t) = ψ(x, y, z, t),

ψ(x, y + L ,s,t) = ψ(x, y, z, t),

ψ(x, y, z + L , t) = ψ(x, y, z, t).

Eq. ( 7-6 ) : ψ(z, y, z, t) = A * exp( i*k_x*x + i*k_y*y + i* k_z*z - i*w*t )

Eq. ( 7-7 ) : k_x = n_x*( 2pi / L ),

  k_y = n_y*( 2pi / L ),

  k_z = n_z*( 2pi / L ).

Answer 1