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LarryC
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- Homework Statement
- Find a general formula to the first order of the inter-particle interaction for the energy of an N+1 particle system of spin-1/2 fermions with one particle of momentum p outside of an N-particle Fermi sea.
- Relevant Equations
- Second quantization of fermions
(Simplified version of Baym, Chapter 19, Problem 2)
Calculate, to first order in the inter-particle interaction V(r-r'), the energy of an N+1 particle system of spin-1/2 fermions with on particle of momentum p outside an N-particle Fermi sea (quasiparticle state). The answer should be expressed as the difference of the energy of the specified state and the energy of the N-particle ground state. (Probably the easiest way is to use creation and annihilation operators to express the difference as the matrix element of a difference of operators - a difference that can be simplified using anti-commutation relations.)
Calculate, to first order in the inter-particle interaction V(r-r'), the energy of an N+1 particle system of spin-1/2 fermions with on particle of momentum p outside an N-particle Fermi sea (quasiparticle state). The answer should be expressed as the difference of the energy of the specified state and the energy of the N-particle ground state. (Probably the easiest way is to use creation and annihilation operators to express the difference as the matrix element of a difference of operators - a difference that can be simplified using anti-commutation relations.)