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

Degree

Reg. No.:

2092    |02 23 C7j

(For the candidates admitted from 2002 and onwards) M.Sc. DEGREE EXAMINATION, NOVEMBER 2003.

First Semester Physics

QUANTUM MECHANICS I Time : Three hoars    Maximum: 100 marks , SECTION A (20 x 1 = 20 marks)

Answer ALL the questions.

Choose the correct answer:

1. If the vectors A and B are orthogonal, {A1B) is equal

la) zero    (b) 1

|c) ~1    (d) none of the above.

2, Energy of He atom by variation method (taking z-atomic number; B_u~ pound slate energy of H-at&m)

is given by

* (a)    (b)

.Cc) (a+VW* m

3, iransition probability/unit time, when transitions are extended to mnimxxxm is given by x where t is

equal to,

(a) 2* [ffi,|p<,) (b)

; <c)    TO .H i,f p(m).

* *i '

4'. Eigen value of J is '

(a) k%(i + l)    ft) /i²s(s+l).

(c) ft*jU+i)    (d) n^zjij+if,

5, Trace of Dirac's matrices is

(.a) +1    (b) zero

Fill in the blanks:

6. If f is a complex number, and if jll) j A) then

(ii| is given by

7 Best energy of Helium occurs using variation

rather than z.

8.     The conclusion of sudden approximation when Hamiltonian changes for a very short finite interval of time, the wave function--.

9.    Eigen value of J_t is f"-,

10.    The order of Dirac's matrices can be only--

Match the following:

(a)

12, Energy of I-arder time (b) Collision of gas

independent non degenerate perturbation

.13,. Application of adiabatic (c) hJ_t if

approximation

14.

15.    , in KG equation

3    2092

Answer in 1 or 2 sentences :

16,    Give example for basis in Hilberts space,

17.    How does first order perturbed wave function m

.time independent case is approximated?

18,    Give one example application 'for the theory of time dependent perturbation.

19.    What is result of    '

20.    Give two examples fcr spin V particle.

SECTION B - *5 x 6 * 80 marks)

Answer ALL the questions choosing either (r) or (b),

21,    (a) Give the comparison between Heisenberg and Dirac (Interaction) picture.

Cr '

(b) Obtain energy eigen values for one dimensional harmonic oscillator.

22.    (a) Give the theory of WKB approximation.

Or

Cb) Obtain ground state energy of Helium atom by perturbation technique.

23,    fa) Give the theory of adiabatic approximation and calculate transition probability.

Drib) Discuss time dependent perturbation theory to potential scattering.

24.    (a) Prove J_t ) ~ ( 1)ft J_tV_Jm .

Or

(b) Obtain matrices for J^s, J_x, J_y and J_z.

25,    (a) Outline the properties of y -matrices.

Or

Cb) Discuss the commutation relations of Dirac's matrices.

5    2092

SECTION C 5 * 10 - 50 marks)

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

26,    (a) Discuss Kronig-Penny mode! for the periodic

potential.

Or-

(b)' Deduce equfttor. ot motion in Schrodinger picture and discuss the properties of the Schronginger picture.

27,    (a) Apply variation, method to Ha molecule and discuss.

Or

Cb) Calculate scrgy eigen value and gnercnr, eigen function for th=> I order time independent non-degenerate perturba;:;r. case,

a-

28,    (a) Give the theory of time dependent perturbation -1 order.

Or

(b) Calculate the transition probability/unit time using time dependent perturbation theory.

6     2092

%

Or

(b) Calculate C.O. coefilcieats for = A; j_a vi.

2 2

80. (a) Obtain Diracs equation ia electromagnetic field.

Or

(b) Derive K.G. equation for H-atom,

Attachment: bharathiar-university-2003-m-sc-physics-19830-1.pdf bharathiar-university-2003-m-sc-physics-19830-2.pdf bharathiar-university-2003-m-sc-physics-19830-3.pdf bharathiar-university-2003-m-sc-physics-19830-4.pdf

Earning:   Approval pending.