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1bHO

One-electron atom

1. Follow the one-electron atom example in the first chapter of Moshinsky (Attach:moshinsky_ch1.pdf)
   • Formulate the Hamiltonian using the dimensionless coordinates.
   • Expand the wave function in harmonic oscillator (HO) basis states: nlm (with l=m=0).
   • Express the Schrödinger equation in matrix form and evaluate the Hamiltonian matrix elements
   • Find the ground state for a single basis state (n=0); vary the HO frequency to find the minimum
   • Introduce more basis states: n=0,1,2,...,N; evaluate the matrix and diagonalize; study the ground state energy as a function of N.
2. Express the Hamiltonian in second quantized form
3. Perform transformation to quasi-spin formalism for use on quantum computer.