Explain the significance of the pseudogap phase in cuprates.
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Calculate the inter-atomic equilibrium distance re for for which the equilibrium lattice energy is
,
and the Madelung constant is 1.75.
In Sommerfeld free electron theory, show that at a temperature T
(i) and (ii)
For the energy dispersion relation:
calculate the inverse mass tensor.
For the hydrogen molecule which has two hydrogen atoms each with one electron occupying the 1s energy level, write the two particle wave functions for the singlet and triplet states. Determine the eigenvalues of the effective Hamiltonian
For a superconducting specimen, the critical fields are and
at
and
respectively. Calculate the critical temperature and critical field at
.
The susceptibility of is
and its density is
. Calculate its total polarisability. Assume that the mass number for
is 32.
Calculate the energy dispersion for s-band in the bcc lattice for the tight binding approximation.
Note: For the central atom located at (0,0,0) in the bcc unit cell, the nearest neighbours are located at , where a is the lattice constant.