(5 points) Suppose we have a modified H atom. For example we put an H atom...

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(5 points) Suppose we have a modified H atom. For example we put an H atom in a strong laser electric field, and the orbital distorts. Take Ytrial = c1100C2Y200+ C3210 i.e. The normalized H atom orbitals for 1s, 2s, and 2pz. The quantum numbers are nlm. (a) There is only one electron, but we know the Hamiltonian of the system is a more complicated potential, not a simple spherical coulomb potential. First write out the variational principle energy in detail. Then write out the set of secular equations that will solve the variational energy, where C1, C2, C3 are the variational parameters. In order to get this set of equations, what has been done to the energy & with respect to C1, C2, C3? (b) Reformulate this in terms of Hij and Sij = Sij terms, and then give the determinantal equation that would minimize the energy . Essentially we are finding the set of c that minimize &. Do not solve. We would find the lowest root of for this determinant. (5 points) Suppose we have a modified H atom. For example we put an H atom in a strong laser electric field, and the orbital distorts. Take Ytrial = c1100C2Y200+ C3210 i.e. The normalized H atom orbitals for 1s, 2s, and 2pz. The quantum numbers are nlm. (a) There is only one electron, but we know the Hamiltonian of the system is a more complicated potential, not a simple spherical coulomb potential. First write out the variational principle energy in detail. Then write out the set of secular equations that will solve the variational energy, where C1, C2, C3 are the variational parameters. In order to get this set of equations, what has been done to the energy & with respect to C1, C2, C3? (b) Reformulate this in terms of Hij and Sij = Sij terms, and then give the determinantal equation that would minimize the energy . Essentially we are finding the set of c that minimize &. Do not solve. We would find the lowest root of for this determinant.