Find an upper bound on the energy of the first excited state of the hydrogen atom. A trial function with ℓ = 1  will automatically be orthogonal to the ground state (see footnote 6); for the radial part of Ψ you can use the same function as in Problem 8.19.

Data from in Problem 8.19.

Find the lowest bound on the ground state of hydrogen you can get using a gaussian trial wave function

where A is determined by normalization and b is an adjustable parameter.

Transcribed Image Text:

(r) = Ae-br²2.