Consider a wavefunction given by:
If the wavefunctions normalised, show that
is also normalised.
We are given that the wavefunction in position space is expressed as a Fourier transform of the momentum-space wavefunction: $$ \Psi(x,t) = \frac{1}{\sqrt{2\pi\hbar}} \int_{-\infty}^{\infty} e^{i(p_x x - E t)/\hbar} \Phi(p_x,t) \, dp_x $$ --- ### Step 1: Given that $\Psi(x,t)$ is normalized This means: $$ \int_{-\infty}^{\infty} |\Psi(x,t)|^2 \, dx = 1 $$ Our goal is ______ ____ ____ _____ ______ _____ ___ _________ __________ ____.
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Write the electronic configuration of HF, HCl, and LiF molecules, hence obtain the bond orders. Draw the schematics of the molecular orbitals and atomic orbitals for each molecule.
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 .
Determine the term symbols associated with a two electron configuration
where . Write the term symbols in order of increasing energy using Hund’s rules.
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.
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.
Prove that the spin function symmetric with respect to the exchange of the two electrons.
Explain the Linear Combination of Atomic Orbitals (LCAO) method for constructing the molecular orbital of the ion. Derive the expression for the ground state molecular orbital and discuss how the overlap integral affects the bonding.