QUANTUM MECHNICS (PREVIOUS SET QUESTIONS)

  Module 3. Quantum Mechanics

  Wave-particle duality. Schrodinger equation (time dependent and time- independent). Eigenvalue problems (particle in a box, harmonic oscillator). Tunneling through a barrier. Wave-function in coordinate and momentum representations. Commutators and Heisenberg uncertainty principle. Dirac notation for state vectors. Motion in certain potential: orbital angular momentum, angular momentum algebra, spin, addition of angular momenta. Hydrogen atom. SternGerlach experiment. Time-independent perturbation theory and applications. Variational method. Time dependent perturbation theory and Fermi’s golden rule, selection rules. Identical particles, Paulis exclusion principle, spin-statistics connection, WKB approximation. Elementary theory of scattering: phase shifts, partial waves, Born approximation. .

PREVIOUS YEAR QUESTION PAPER

SET 2019/7

46. A ‘free quantum mechanical particle’ is represented by a ---------.

A) plane wave with definite wavelength

B) spherical wave

C) exponentially decaying wave

D) none of these

47. Expectation value of a dynamical variable are in general -------.

A) functions of space

B) functions of time

C) not functions of space and time

D) constants

50. For a particle confined in a rectangular potential well with finite walls, (E<V) which among

the following is NOT TRUE?

A) energy eigenvalues are discrete

B) wave functions are symmetric or antisymmetric about the symmetry point

C) wave function vanish at the boundary of the well

D) minimum energy permitted is not zero

51. For a particle confined in a two dimensional square well with impenetrable walls the ----

A) ground state has two fold degeneracy

B) ground state is non degenerate

C) first excited state is non degenerate

D) all energy states are degenerate

52. For a particle confined in a one dimensional finite square well centered at x = 0 and

width 2a, the expectation value of position when it is in the ground state is -------.

A) x= a/2     B) x=0     C) x=a/4     D) none of these

53. Which among the following statement is TRUE?

A) If two Hermition operators commute they have simultaneous eigen values

B) Hermition operators can have both real and imaginary eigen values

C) For Hermition operators eigen functions corresponding to two different eigen values are orthogonal

D) None of these

54. For a particle confined in a one dimensional square potential well of infinite height and a

one dimensional harmonic oscillator the quantum number corresponding to ground state are

---------respectively.

A) 1 and 1    B) 1and 0    C) 0 and1    D 0 and 0

55. Which among the following commutation relations is TRUE?

A) [Y,LY] = 0      B) [Y,LZ ]= 0    C) [Y,LX]= iℏZ     D) none of these

#X,Y,Z, REPRESENT COORDINATES

#L REPESENT LINER MOMENTUM

56. Which among the following dynamical variables can have half integer quantum numbers?

A) linear momentum of a particle confined in a square well

B) total energy of one dimensional linear harmonic oscillator

C) orbital angular momentum of a quantum mechanical particle

D) total angular momentum of a quantum mechanical particle

57. Which among the following techniques can be used for calculating the ground state energy of He atom?

A) Time dependent perturbation theory    B) Variational principle

C) Harmonic approximation                      D) Bloch theorem

58. Origin of electronic energy bands in a crystalline solid can be qualitatively accounted

using

A) Time independent perturbation theory

B) Time dependent perturbation theory

C) Kronig-Penny model            D) Variational principle

59. The wave function corresponding to a system consisting of two identical particles is  symmetric with respect to exchange operation, then the one value possible for intrinsic   angular momentum in unit of ħ is ------.

A) 1/2         B) 1     C) 3/2           D) none of these

91. What is the value of [Lz , L^2]?

A) 1    B) L2           C) (Lx + Ly)      D) 0

95. Consider a one dimensional infinite square well of width 1 cm with free electrons in it. If

its Fermi energy is 2eV, what is the number of electrons inside the well?

A) 46.2×107 B) 462×107 C) 0.462×107 D) 4.62×107

SET 2019/2

26. The energy of an electron in the energy level (121) in a cubical potential box of side 1 Å is

A) 1.13 eV   B) 2.25 eV     C) 226 eV     D) 11.2 eV