1000 Solved Problems in Modern Physics

3.3 Solutions 177

Fig. 3.10η−ξcurves for class II solutions. For explanation see the text (After Leonard I. Schiff,
Quantum mechanics, McGraw-Hill 1955)

ForV 0 a^2 between 2π^2 ^2 / 8 mand 4π^2 ^2 / 8 mthere is one energy level of

each class or two altogether. AsV 0 a^2 increases, energy levels appear succes-

sively first of one class and next of the other.

3.26 The probability for neutron and proton to be found outside the range of nuclear
forces (refer to Problem 3.21)

P=

∫∞

R

|ψ 2 |^2 dτ=

∫

(|u 2 (r)|/r)^24 πr^2 dr

= 4 πC^2

∫∞

R

e−^2 γrdr

P= 2 πC^2 e−^2 γR/γ (1)

By Eq. (15) of solution 3.19

AsinkR=Ce−γR

or

C^2 e−^2 γR=A^2 sin^2 kR≈A^2 (2)

because,kR≈π/ 2

Therefore,

p=

2 πA^2

γ

(3)

We can now find the constantAfrom the normalization condition