Quantum wormhole with conformal scalar field

In this paper I use the Hartle-Hawking method to discuss quantum wormhole with conformal scalar field. I derive the corresponding Wheeler-De Witt equation, calculate the wormhole wave function, which is found to be the product of two harmonic solutions. Analysis of the wave function reveals that the probability density of the wormhole appearing at a = 0 is zero, that the most probable radius of the wormhole base state is the Planck length and that the wormhole is mostly likely to be in a state of small Φ value.