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Sample Topics

Q1. Classical physics vs. Quantum mechanics.When does classical physics become quantum mechanics?and when can’t we use classical physics; when do we use quantum mechanics?

Q2. Did Einstein support quantum mechanics as being fundamental physics, or did he think quantum mechanics was incomplete?

Q3. Are there real applications for using delta function potentials in quantum mechanics (other than using it as an exactly solvable toy model in introductory undergraduate quantum mechanics textbooks) ?

Q4. One important application of Quantum Mechanics is laser technology. Construct an information pamphlet including

– Uses of laser technology

– How it applies quantum mechanics

– Advantage/disadvantages of laser technology

Q1. An insulating spherical shell of radius R carries a uniform electric surface charge density σ . It rotates with angular velocity Ω about its center

(a) Find the current density K(r,θ,ϕ) resulting from the rotation (in spherical coordinates).

(b) Find the magnetic dipole moment m of the sphere.

(c) Show that for r > R (outside the sphere) the vector potential A(r,θ,ϕ) is exactly that of a perfect dipole, so that a spinning sphere produces a perfect dipole field, with no higher multipole contributions.

Q2. Electrodynamics: How are the boundary conditions related to the potential different for capacitors vs. linear dielectrics?

Q3. What is Maxwell’s contribution to the 4 most important electrodynamic equations? Explain completely.

Q1. Polarization of the Normal Modes of a Monatomic Bravais Lattice

(a) Show that if k lies along a 3-, 4-, or 6-fold axis, then one normal mode is polarized along k, and the other two are degenerate and polarized perpendicular to k.

(b) Show that if k lies in a plane of mirror symmetry, then one normal mode has a polariza-tion perpendicular to k, and the other two have polarization vectors lying in the mirror plane.

(c) Show that if the point k lies in a Bragg plane that is perpendicular to a plane of mirror symmetry, then one normal mode is polarized perpendicular to the Bragg plane, while the other two have polarizations lying in the plane. (Note that in this case the modes cannot be strictly longitudinal and transverse unless k is perpendicular to the Bragg plane.) To answer these questions, one must note that any operation that leaves both k and the crystal invariant must transform one normal mode with wave vector k into another. In particular, the set of three (orthogonal) polarization vectors must be invariant under such operations: in applying this fact one must remember that if two normal modes are degenerate, then any vector in the plane spanned by their polarization vectors is also a possible polarization vector. Q2. Using the Debye approximations for one- dimensional monatomic lattice with atomic spacing a and sound v, show thatD = v /a and D = h D / KB

Q3. Derive the integral expression for the thermal energy and phonon heat capacity. show thatCv= 2 KB (T/ D) / 3a per unit length at low temperature =KB / a per unit length at high temperature.

Q4. A weak periodic potential in the form of V(x) = V0 cos(2 kF x) is created for a one-dimensional electron system (kF is the Fermi wavenumber). Calculate E(k) for the lowest energy band, and determine the total energy of the system at zero temperature as a function of V0.

Q1. What is the difference between atomic line spectra and molecular/emission spectra?

Q2. Explain at the atomic/molecular level why each of the following are generated:

- line spectra
- band spectra
- continuum spectra

Q3. Discuss types and nature of atomic spectra.

Q4. What is the atomic spectra experiments, and what information is obtained by these experiments?

Q5. What are the similarities between the Bohr model and the atomic spectra equations?

Q1. Why do statistical mechanics not apply to nonideal gases?

Q2. Using the statistical mechanics of photon gas, How is it possible to derive the spectral density of a black body?

Q3. Why should the equilibrium constant be dependent on the difference in Gibbs energy? How is this relationship described using statistical mechanics?

Q4. A generalized form of the equation of state for gases that can be derived from the methods of statistical mechanics is called the____________ equation of state.

Q1. In an undisturbed ore containing .1% by weight of Uranium-238 there will be some Radium-226. Calculate the weight of this isotope of radium to be found in one metric ton of ore. What is the rate of generation of helium gas in kg per year in this amount of ore?

Q2. What is the Physical basis of the independent-particle model of the nucleus?

Q3. Because pions had not been discovered in 1936 when yukawa proposed the meson theory of the nuclear force, it was suggested that the meson was yukawa’s particle. what would the range of the nuclear force be if this were true?

Q4. Discuss the advantages and disadvantages of nuclear physics.

Voice of Experts

Ahamad Shakil

Student MS- FY, IISER Bhopal

Srinath Polineni

Ph.D Scholar - Andhra University

Anuj Patel

Student, NIT Agartala

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