Page 81 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

Differential and Integral Equation

Notes 3.8 Review Questions

x
x
1. Use the Rodrigue s formula to drive the Hermite polynomials H 2 ( ) and H 3 ( )
2. Evaluate

x
x e x 2 H ( )H ( )dx
x
2 3
3. Show that
H 1 ( ) 2xH 0 ( )
x
x
4. For what value of ,n H n (0) 0?
5. From generating function show that

H ( ) 32x 5 160x 3 120x
x
5
Answers: Self Assessment

1. Terminating

2. Finite
3. n
4. 12
x
5. H 2 ( ) (4x 2 2)

dH n ( )
x
x
6. 2nH n 1 ( )
dx
8. b
9. H 2 ( ) 4x 2 2, H 3 ( ) 8x 3 12x
x
x
10. 4
11. Zero

3.9 Further Readings

Books K. Yosida, Lectures on Differential and Integral Equations
L.D. Landau and E.M. Lifshitz, Quantum Mechanics

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