Atoms
For standing waves y(x,t)=Asin(kx)cos(?t)
y(x,t)=Asin(2?x/?) cos(?t)
y(x=0,t)= 0 = y(x=L,t) => 2?L/? = n? =>?=2L/n
=> only certain frequencies f=v/?= nv/2L=nf1
Matter waves: P(x,t) =0 outside box
P(x,t)= |A`|2 sin2(kx) => need P(L,t)=0
kL =(2?/?)L = n ? => ? = (2L)/n “standing waves”
only certain ? => only certain p => discrete energies