Question: Wavefunctions and Probabilities Consider the ground-state coordinate-representation wavefunction for the electron in a Hydrogen Atom: (r, , ) = Ne^(r/a0) since there is no or

Wavefunctions and Probabilities Consider the ground-state coordinate-representation wavefunction for the electron in a Hydrogen Atom:

(r, , ) = Ne^(r/a0)

since there is no or dependence in this function, the system is spherically symmetric and thus the angular dependence of of the function is constant.

(a) Choose a value of N such that the wavefunction is normalized over all space.

(b) Find the probability that the electron is within a sphere of radius a0 centered at the nucleus.

(c) What is the expectation value of , hi, in this state?

(d) What is the uncertainty in , , in this state?

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