Question

Explain the variational approach to finding approximate eigenenergies of a Hamiltonian. What are the advantages and disadvantages of this approach compared to the time independent perturbation theory. Explain the single parameter variational method and the linear combination of states method.

Answer 1

Advantage:-

When time independent perturbation theory fails (If the results are corresponding to Ho are not know of for Hp ) then variational method is used

Disadvantage:-

It's used to calculate energy of ground state and few excited state when H of the system is known and corresponding eigenfunction is not known.

SINGLE PARAMETER VARIATIONAL METHOD :-

* For ground state :-

1) Choise of trial wavefunction:-

For the choise of trial wave function include all known properties like no. of nodes, parity,behaviour of the function at infinity etc through position variable and include all unknown properties through a parameter ( alpha) know as variational parameter.

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