BSc Physics SEM IV ATKT 2018-19 ATKT Physics II Question Paper - Mumbai University | munotes

Questions asked in this paper

• (2) Figures to the right indicate maximum marks

1. Q2 ) Attempt any one How does de Broglie postulate enter into Schrodinger’s theory? 2 equation of continuity in quantum mechanics and discuss its significance 8 marks
   • B) Attempt any one 1 Max Born interpretation of wave mechanics. Hence explain ‘Normalization of 8
   • C) Attempt any one Find the expectation value of particle position if the eigen function describing the particle is given by 2 that for stationary states, expectation of momentum is independent of time 4
2. Q3 <A) Attempt any one 1 A particle is subjected to a three dimensional box and is subjected to a potential given inside the box outside the box Write down Schrodinger’s time independent wave equation and obtain normalised 2 an electron of energy E incident on the potential step defined by Show that the particle can penetrate into the second region even if its energy is less 8 marks
   • B) Attempt any one Set up Schrodinger’s equation for a free particle. Solve the equation to obtain the eigenfunction. Show that the expectation value of momentum of the particle is same as the momentum that a classical particle will have 2 Consider a particle confined to move in an infinite rectangular potential well. Show that expectation value of the position co-ordinate x of a particle in the well depends upon the length of the well 8
   • C) Attempt any one 1 of kinetic energy 5 MeV tries to enter a nucleus and its potential energy drops at the nuclear surface very rapidly from a constant external value V = 0 toa constant internal value V = — 50 MeV. Estimate the probability that the neutron will be reflected at the nuclear surface 2 Ana particle having energy 10 MeV approaches a potential step of height 50 MeV and width m. Determine the transition coefficient if mass of particle is 6-68 x 4
3. Q4 <A) Attempt any one | State correspondence principle. Show how quantum and classical probabilities of a one-dimensional oscillator leads to correspondence principle 2 in detail the penetration of particle having energy Eo across potential barrier of finite height Vo and width (a) for the case Eo > Vo 8 marks
   • B) Attempt any one 1 Show that the STIE for a one-dimensional harmonic oscillator can be written in the 2 the Schrodinger’s equation for linear harmonic oscillator and solve it to obtain its eigen value and eigen function 8
   • C) Attempt any one 1 Ana-particle having MeV approaches a potential barrier of height 30 MeV Find the width of potential barrier if the transmission coefficient is 2 x (Given: mass of a-particle = 6.68 x 2 A beam of electrons is incident on a potential barrier SeV high and 5A wide. What should be their energy so that half of them tunnel through the barrier? Attempt any Four (20) Write a short on ‘Operators 2 ‘Wave functions add, not the probabilities’, explain that the eigen functions of a quantum mechanical operator with different eigen values are orthogonal 4 particle arrives at a step potential having height Vo. Discuss the problem classically when energy of the particle is 4
   • (i) more than the step height ( ii ) less than the step height The wave function for the ground state of a harmonic oscillator of mass m and force constant k is proportional toe” where a? = and w? = . Show that this is a solution and find the corresponding eigen value 6 the expectation value <x> for the first excited state of a simple harmonic

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