Question

a) Show that the n=1 and n=2 states of the particle-in-a-box are orthogonal. b) Show that the n= 0 and n= 1 states of the harmonic oscillator are orthogonal. c) Show that the 1s and 2s states of the hydrogen atom are orthogonal.

Answer 1

wave funstigu for, nol for, n=2 and J는 cos 뜨는 for ert hogomel.condition L/2 니2 Ssinn cosusn -L12 25 Cos 3An sin Kn -L[뉴[- cot 목] - 늦 [o(g)-w-(5 ar crdho gonad harmonic oscilleteh- 22 e 21? functi n for wane for forni= Tano fiin) = ta lbe as (oustat = a t00 %3D no2 in This Juncinm in oddfuntigen so, Pi,2 aro erthagon al Jadd fare dnao Shot on realme C2

for hudiogen atom wan funetiou- for P1o = Por enthagonal doesn't play any hall here. where IP,2 alo Cons dauta Conoli lipu Jo, 10 (2-5)* (2- PL dr 290 let do 2andn (2- e (2 ndn) -322 290 3x2 fitz 23 240 290 bns taut x (4ln-1)]! =c{013>0 and -A n2 =3(213=!20 Y2 = 2P20-0)20 abo rthag oual. t on realme C2