Question

Determine for an electron in a 2 Dimensional box two pairs of quantum numbers which will cause degenerate energy given the following parameters:

L_x= 2nm

L_y = 3nm

Answer 1

As (2, 6) and (4, 3) has same energy value in this rectangular box, thus for this case (2, 6) and (4, 3) are two degenerate pairs of quantum numbers.

aquations for 2D x wave we come toU know thad to tul energy whore h-Planck 2 LO nstant m- Mas of electron x, ny= 1,2,3... . x Ex,3 (D 8 m 2- length of box x -axis 2 h ng nx 13 Ly Length of tox Exym h nt 4n.y 2 36 Ey 8 m x36 И 8 mx3 Constand EMK On24nj from the definition of degeneay tahen diferant shat of the system acquire (on10K coe know that same tay wne called degentatid enry stle nergy then Now E,I 9.1 4 13 K K .! K (9.12 ) 25 K E1, 2 4. 2 = K (9.2 + 4.1) E21 40 K K (3.22+ 4.252 K (3.3 42) 9-2+ 4.3)72 K E 2,2 - 97 K E3 2 - K E = K 2,3 So have to on Noo, to find out dogenracy errro mthod,bPuting nl, 2, 3 And bydoing these we ry and ue Cwe K +4 E,6