Final answer:
The probability of finding an electron between x = 0.99a0 and x = 1.01a0 when it is in the ground state in a one-dimensional Coulomb potential is determined by integrating the squared wavefunction over that region.
Step-by-step explanation:
The student is asking about the probability of finding an electron in a specific region of space when it is in the ground state associated with a Coulomb potential, which is typical for the hydrogen atom. To calculate the probability, one would use the square of the wavefunction (ψ2), integrated over the given spatial range. Here, the range is between x = 0.99a0 and x = 1.01a0, where a0 is the Bohr radius. The probability is given by the area under the radial probability density function, P(r), within the specified interval.
For the ground state of a hydrogen-like atom, the radial probability density function is given by P(r) = (4/πa03)r2 exp(−2r/a0). This function reflects the probability density of finding the electron at a distance r from the nucleus. Integrating P(r) from 0.99a0 to 1.01a0 will give us the probability in question. The integral involves exponential and polynomial terms which are related to the behavior of the electron in the Coulomb potential.
It is important to note that such a calculation would involve advanced knowledge of integrals and quantum mechanics, specifically the quantum behavior of particles in potential wells, and exact numbers would come from performing the actual integration of the probability density function.