Question: For the hydrogen atom and the trial function e-where a is a variational parameter, using atomic units, calculate the expectation values of the potential energy

For the hydrogen atom and the trial function e-where a is a variational parameter, using atomic units, calculate the expectation values of the potential energy (the operator is - ) and the kinetic energy (the operator is 2r dr "ar ) as functions of a. Add these to get the energy as a function of a, find the value of a for which the energy is minimum, and calculate the energy for this value of a. (In your integrals, don't forget to include the r factor from the from the spherical coordinates volume element.) dr : 1/2 2 -ar 1 dr 2 a -ar 1 re dr= (TL ; 1/2 4 a a O' 1 dr= 2a -ar 3 74 . 1/2 8a

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