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Pune University - Pune University - Sem - II : Quantum Mechanics II, April 2010 (Old Course)

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Total No. of Questions : 7] P877 [Total No. of Pages : 2 [3722]-24 M. Sc. PHYSICS PHY UT - 604 : Quantum Mechanics II (Old Course) (2005 Pattern) (Sem. - II) Time : 3 Hours] [Max. Marks : 80 Instructions to the candidates : 1) Question No. 1 is compulsory. 2) Attempt any four from remaining. 3) Draw neat diagrams wherever necessary. 4) Figures to the right indicate full marks. 5) Use of Mathematical tables and calculators are allowed. Q1) Attempt any four from following : a) Find the Eigen values of exchange operator P12 for identical particles.[4] b) Discuss validity conditions of W.K.B. approximation. c) Show that the total energies in Laboratory and centre of mass system is related by Tcm = m2 TLab . m1 + m2 [4] [4] d) Discuss the selection rule for electric dipole approximation. e) What is perturbation? Develop first order perturbation equations for stationary states. [4] f) Discuss role of symmetry in quantum mechanics. [4] Obtain Slator s determinant for system of N electrons. [8] Q2) a) [4] b) Explain the term differential cross section. Show that differential cross section is directly proportional to scattering amplitude. [8] Q3) a) Using variation method obtain an expression for ground state of hydrogen atom. [8] P.T.O. b) Prove that total = 4 I m f (0 ) k Where f (0 ) is imaginary part of the forward scattering amplitude. [8] Q4) a) What do you mean by partial waves? Obtain the partial wave shift l for scattering from square well potential. [8] b) Develop time dependent perturbation theory to obtain first order correction to amplitude a(f1) (t ) . [8] Q5) a) Compare classical and quantum mechanical treatment for scattering of identical particles. [8] b) Using WKB approximation, obtain the transmission coefficient for particle. [8] Q6) a) Obtain first order equation of time independent perturbation theory. Consider a doubly denerate level and show that the perturbation removes degeneracy. [8] b) Deduce the expression for scattering amplitude using Born approximation for Yukawa Potential. [8] Q7) a) Explain principle of variation method. Show that it leads to better estimation. [4] b) What are symmetric and antisymmetric wave functions? [4] c) Describe vectors and pseudovectors in terms of intrinsic parity. [4] d) Discuss the centre of mass and laboratory frame of reference with respect to scattering cross section. [4] rrrr [3722]-24 -2-

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Additional Info : M.Sc. PHYSICS, PHY UT - 604 : Quantum Mechanics II (Old Course) (2005 Pattern) (Semister - II), Pune University
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