Question

A good trial function for the ground state of the Hydrogen atom is ?? = Ce^{-?r} with C = ?(?³/?). a) Write down the Hamiltonian for the electron in a simple Hydrogen atom (e.g. One proton and one electron). b) Use the Rayleigh-Ritz method (also known as the variational method) to write down the ground state energy and ground state wavefunction.

          A good trial function for the ground state of the Hydrogen atom is
?? = Ce^{-?r}

with C = ?(?³/?).

a) Write down the Hamiltonian for the electron in a simple Hydrogen atom (e.g. One proton and one electron).

b) Use the Rayleigh-Ritz method (also known as the variational method) to write down the ground state energy and ground state wavefunction.

A good trial function for the ground state of the Hydrogen atom is
?? = Ce^-?r

with C = ?(?³/?).

a) Write down the Hamiltonian for the electron in a simple Hydrogen atom (e.g. One proton and one electron).

b) Use the Rayleigh-Ritz method (also known as the variational method) to write down the ground state energy and ground state wavefunction.

Added by Cassandra S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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A good trial function for the ground state of the Hydrogen atom is ψα = Ce^{-αr}, with C = √(α³/π). a) Write down the Hamiltonian for the electron in a simple Hydrogen atom (e.g. One proton and one electron). b) Use the Rayleigh-Ritz method (also known as the variational method) to write down the ground state energy and ground state wavefunction.