Question

The particle in a one-dimensional box does not exhibit degeneracy; a particle in a two-dimensional square box does as demonstrated in the text. The lowest energy level that shows degeneracy is E1,2 E2, 5h/(8mL2). What is the next lowest energy level that exhibits degeneracy and what is the degeneracy

Answer 1

The particle is a one - dimensional box does not exhibit decency is a particle in a two dimensional square box does as demonstrated in the text . The lowest energy level that shows degeneracy is E_1, 2 = E_2, 1 = 5 h 6 2/ 2 m L^2 what is the next lowest energy level that exhibits degeneracy and what is the degeneracy Degenerate state a given when two different wave function correspond to same energy level for a 2-0 square the energy is given as e_n_m, n_g = h^2/ 2 m h^2 (m x^2 + n Y^2) where n = 1, 2,... lowest value of n = 1 so putting n_x = 1 , n_y = 1 E_m_1, n_2 = h^2/Q m L^2 (1 + 1)

Next degenerate level arises at (3,1) and (1,3) and degeneracy is 2.