Potential energy of mass m is U(x)=Eₒ,when 0≤x≤1, =0when x≻1.The total energy of the particle is 2Eₒ. The De Broglie wave length of the particle is λ₁ when 0≤x≤1 and λ₂ when x≻1. what is the ratio of λ₁ and λ₂ ?
1 Answer
Jun 18, 2018

For
#x in [0,1]# , total energy is#E_1 = 2 E_o# , and potential energy is#U_1 = E_o# . So kinetic energy is#T_1 = E_1  U_1 = E_o# 
For
#x in (1,oo)# , total energy again is#E_2 = 2 E_o# , but potential energy is#U_2 = 0# . So kinetic energy is#T_2 = 2E_o# 
#implies T_2/T_1 = 2#
From the deBroglie relation
#lambda = h / sqrt(2mT) qquad :. lambda propto 1/sqrtT#