Bharathiar University 2003 M.Sc Physics Quantum Mechanics -II - Question Paper

Degree

25.    (a) Distinguish between classical field and quantum field. Discuss quantaisation of wave fields,

Or

(b) Write down the. Hamiltonian equations. Explain quantaisation of electromagnetic field energy,

SECTION C (5 x 10 * 80 marks)

Answer ALL questions choosing either (a) or (b),

26.    (a) Deduce Greens function for a free particle.

Or

, ' (b) Discuss scattering by a eoulotcb potential.

27.     (a) Outline the main features of Thomas Fenftt model

Or

(b) Diocuss Hannreej elf consistent model,

8, (a) Dcil*e cat*g>* value and eigen functions for the case of a hydrogen molecule ion.

Or

(b) Describe spin orbit interaction correction.

29.    (a) Describe semiclassieal theory of radiation and calculate Easultonian of charged partide in an &.m,

.field.

Or

(b) Calculate emission rate and absorption rat#,

30.    (a) Obtain quantum equation for tlie field quantisation.

Or

(b) Derive classical lagrangian equation.

\.

7    2093

Beg, No, i

102S 368]

(For the candidates admitted from 2002 awards)

M.Sc. DEQUE EXAMINATION, HOSS 2003.

Second Semester Physics

QUANTUM MECHANICS II

Maximum: 100 marks

SECTION A (20x1 20 marM)

Answer ALL (pimmm.

Choose tha eorreefc answer T

1. Reduced Mass⁴/i'inJhejcattermgof aetitrons by pro teas is given by

2, Perturbed Hamiltonian JET in central field approximation is

f&²

fa)

i>j^ra * I ^rt

(b) B' = T---

<>/^ry ^ri

,2

3.    Potential energy minimum of H* ion is,

(a) 0,11m    (b) 5 ev

(c) 1.77 ev ....    (d) 3.54 ev.

4.    * Bohrs angular frequency is -B_m

A

ft.

*41?

w

(d) SazL.

Mm

5. Creation operator & is

(a) (p-immx)

1

(b)

(C)

(d) -j......L=t*(p-imwx),

j2mhw

Fili up th Maaks :

6. The relation connecting scattering amplitude f(0, #) witi differential, scattering cross seetion is

is-.

7. Hartree assumed that the electrons in an atom, move independently in a-.

8. Heiler-London model is based on theory.

I.ity wrrcctiDc for the momentum, j⁵ is

10HaiailtoniaB" sad Lagrangiaa are connected by

2093

Match, the following:

11.    Neutron proton scattering (a)    LCAO

12.    Central field approximation (b)    Einstein

13.    Hydrogen molecule ion (c)    Schrodinger

14.    Traasifcion probability (d)    Self consistent

15.    Quantisation of field (e)    Reduced mass. Answer in one or two sentences :

16.    What is the scattering cross-section value in the case of neutron-proton scaiteredlculated by theory?

17.    What is the value of total spin in the case of hydrogen molecule for stable and unstable state?

18.    Give examples for alkali atom.

19.    Give an example for the type of emission strongly frequency dependent.

20.    What is the value of [c,, Nj) ?

Answer ALL questions, choosing either (a) or (b),

21.    (a) Define scattering amplitude and explain.

Or

(b) Outline the properties of coulomb scattering.

22.    (a) Write down schrodinger equation for an N-electroa system and explain the important terms.

Or

Cb) What km ..the main assumptions of central field approssB&tioa? Explain.

23.    (a) Write a note on co-variant bond.

Or

- (b) Explain the term hybridisation.

24.    (a) Ixplaia the two kinds of emission. Derive Einstein coefficients.

Or

'(t) Outline the properties of density matrix.

s    Mm

Attachment: bharathiar-university-2003-m-sc-physics-19829-1.pdf bharathiar-university-2003-m-sc-physics-19829-2.pdf bharathiar-university-2003-m-sc-physics-19829-3.pdf bharathiar-university-2003-m-sc-physics-19829-4.pdf

Earning:   Approval pending.