Question

2. 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/2).) 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 = 0,1,2,....)

Answer 1

ve) 6 B a A3 2uh e e at 3 e At a dn

e f d e di fLrdiy df ef df 1 1n 2 mi 1t1e8 -1 C7u ノeD d, 2 At

Kt/ be 大hn the Wove unt A owe trunekior NG 大h epp Lt e WNou (A dive -A L e やテレて dn e +2tt)edu t te

tl) , t (tt)e v) evo e e da f lit) vo da v) 2tt) 2 V 2E 2-2- 2-2 e)2 tit) tee 2 + )t)t Th yeysn relati
720p