Consider the bound states (e < 0) of a particle of mass u on the one- dimensional half line, 0< x < oo, with the linear potential, b a + v () where a and b are positive constants (a) what is the asymptotic behavior of the wavefunction as x is useful to define a dimensionless variable. (ans: ~e /24e/ oo. it where u= (b) what is the asymptotic behavior of the wavefunction as a - 0. (ans: b~ where s=+ ++β whereβ = 2μ0 /h ) (c) from the result in (a), construct the series solution for the rest of the wavefunction. what is the recursion relation for the coef- ficients? (ans: 2(k+s)-a ak+1 k+8+1)(k+s)-b where k = 0,1,2, and ak a= (d) find the quantization condition of the energy of the particle. (ans: μα2 en 27 (n+s)where n = 0,1,