  We study the energy representation of conformal quantum mechanics as the
Whittaker vector without specifying classical Lagrangian. We show that a
generating function of expectation values among two excited states of the
dilatation operator in conformal quantum mechanics is a solution to the
Wheeler-DeWitt equation and it corresponds to the AdS2 partition function
evaluated as the minisuperspace wave function in Liouville field theory. We
also show that the dilatation expectation values in conformal quantum mechanics
lead to the asymptotic smoothed counting function of the Riemann zeros.
