MSc Physics (Electronics I) SEM II 2018 19 May 2018-19 PHYSICS PAPER III QUANTUM MECHANICS II (OLD) Question Paper - Mumbai University | munotes

Questions asked in this paper

• (2) Figures to the right indicate full marks

1. Q1 (a) Attempt any one:--- 8 marks
   • (i) | What are Clebsch-Gordan coefficients? Calculate the Clebsch-Gordon coefficients for addition of angular
   • (ii) |s,m,) is the simultaneous eigenstates of S* and Find the matrix representation of operators $,. Sy and in this basis
   • (b) Attempt any one:--- 4
   • (i) Find the matrix representations of and for j = 1 in the |j,m) basis
   • (i) particle is in the state
   • A) Determine A
   • B) What are the probabilities of getting +h/2 and —h/2 if you
2. Q2 (a) Attempt any one:--- 8 marks
   • (i) Explain time independent perturbation theory for non-degenerate states Obtain the first order perturbation correction to the eigenvalues and
   • (ii). A system described by a Hamiltonian with known solution set
   • t)}. Initially (t the system in the state t) subjected to a time perturbation . Obtain the probability of transition of the system from the state t) to (7, t) in
   • (b) Attempt any one:--- 4
   • (i) energy eigenfunctions for the infinite square well of width a is: Find the first order correction to the energies and eigenfunctions for the
   • (ii) Explain Fermi’s Golden rule
3. Q3 (a) Attempt any one:--- 8 marks
   • (i) the variational method to estimate the ground state energy of a particle of mass m in the potential given by Take w(x) = * as the trial wave function where a is the variational parameter and A is the normalization constant
   • (ii) Use WKB approximation to find the tunneling probability through a
   • (b) Attempt any one:--- 4
   • (i) Show that variational method gives the upper bound of the ground state
   • (ii) Obtain energy eigenvalues. of harmonic using WKB
4. Q4 (a) Attempt any one:--- 8 marks
   • (i) Derive the expression of scattering amplitude using partial wave analysis
   • (ii) Calculate the differential cross-section in the Born approximation for the potential V(r) = 2) Also calculate the total cross-section
   • (b) Attempt any one:--- 4
   • (i) Calculate the total cross-section for low energy (S-wave) scattering of a particle of mass m from the following potential
   • (ii) Discuss the validity conditions of Born approximation
5. Q5 Attempt any 12 marks
   • (a) Show that the components of Pauli spin matrices 6 anticommute
   • (b) Calculate: A) B)
   • (c) atom is in a constant uniform electric field ‘E’ that points in the z direction. Calculate the first order correction to the ground state energy of the Given: Unperturbed ground state of hydrogen atom is = e("/ ao)
   • (d) A particle is initially in its ground state in a one-dimensional harmonic potential A perturbation, H’ = is turned on at t = 0. Calculate the probability that the particle will be found in its first excited state after a sufficiently long time
   • (e) Use WKB approximation to estimate the transmission coefficient of a particle of mass m and energy (E < moving through the following potential barrier
   • (f) Explain briefly the Rayleigh Ritz method using a linear combination of fixed basis function as trial wave function and treat the expansion coefficient as
   • (g) Explain optical theorem
   • (h) What is scattering amplitude? How is it related to scattering cross section?

Read from the scan above, so a character or two may differ. The scan is the original.