Prove that the spin function symmetric with respect to the exchange of the two electrons.
We are given the spin function: $$ \chi_+(1,2) = \frac{1}{\sqrt{2}}[\alpha(1)\beta(2) + \alpha(2)\beta(1)] $$ We are to prove ____ __________ _____ ________ _________ ______.
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Consider a wavefunction given by:
If the wavefunctions normalised, show that
is also normalised.
Prove that the spin function symmetric with respect to the exchange of the two electrons.
A Hydrogen atom is in a region of strong magnetic field. How many energy levels will be there corresponding to the unperturbed 2p level of this atom?
Determine the term symbols associated with a two electron configuration
where . Write the term symbols in order of increasing energy using Hund’s rules.
Determine the shift in energy caused by the ‘relativistic correction to kinetic energy’
, the spin-orbit term
, and Darwin term
for n = 2 level of He .
Li ion is placed in an electric field of magnitude
direction. Determine the energy shift for levels with n =1 and n = 2 in presence of this field.
For a non-degenerate time indepedent perturbation, show that the first-order energy shift is equal to the expectation value of the perturbing Hamiltonian in the unperturbed energy eigenstate.