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Fraktal
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Homework Statement
Use leading order perturbation theory to calculate the ground state shift of hydrogen due to perturbation: [tex]\hat{V}[/tex]
Homework Equations
1. Leading terms in expansion of energy:
[tex]E=mc^{2}+\frac{p^{2}}{2m}-\frac{p^{4}}{8m^{3}c^{2}}+...[/tex]
2.
[tex]\hat{H}=\hat{H}_{0}+\hat{V}[/tex]
where [tex]\hat{H}_{0}[/tex] is the Hamiltonian and the leading correction:
[tex]\hat{V}=-\frac{\hbar^{4}}{8m^{3}c^{2}}\Delta^{2}[/tex]
Other useful equations:
1. [tex]\left(\psi_{1},\Delta^{2}\psi_{2}\right)=\left(\Delta\psi_{1},\Delta\psi_{2}\right)[/tex]
2. [itex]\psi_{0,0,0}[/itex] is a solution to the relevant stationary Schrodinger equation.
The Attempt at a Solution
Not sure where to start with this!
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