1. Stationary State Approximate Methods
Chapter 2
WKB Problems Griffith
Dr. Arvind Kumar
Physics Department
NIT Jalandhar
e.mail:

2. Problem 1 (8.1)
Find allowed energies using the WKB method
For following infinite square well

3. Ans: Use
Split integral according to give potential range
And square and finally we will get
In above is =

4. Put in Schrodinger Eq and prove --------(2)
Problem 2 (8.2): Alternative derivation of WKB method
Consider function
----(1)
Put in Schrodinger Eq and prove
(2)
(ii) Expand f(x) as power seried in
--(3)
And show that
------(4)

5. (iii) From eq (4) find f0 and f1 and use that
Eq (1) through (3) and show that

6. Problem 3 (8.3)
Consider particle of energy E which
encounter a potential barrier of height V0
(E<V0) and width 2a. Find transmission
probability using WKB method.
Note: Compare with exact result solving Schrodinger eq:

7. Problem 4 (8.7): Find the expression for the
energy of harmonic oscillator using WKB
method.
Problem 5 (8.11): For power law
Potential
Show that

8. (Central potential)
Energy of a particle bound in central potential V(r)

9. Problem (6): For Logarithmic potential
Use WKB method to find allowed energy. For
this problem consider infinite wall at r = 0.
Hint: Use