For a system without an external poten tial we take 0

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: wavefunction, and project dynamics under Hamiltonian (3.31) into this state . This procedure gives equation (3.34)(we will discuss mathematical formalism for finding such projected equations of motion in section ??. For now we will assume that this statement sounds reasonable). In the simplest case of Vext = 0 we observe that equation (3.34) has a static √ solution Ψcl = n0 eiφ , provided that equation (3.5) is satisfied. Phase φ can be arbitrary. Equation (3.33) can be used to obtain an alternative derivation of the spectrum of Bogoliubov quasiparticles. For a system without an external poten√ tial we take Ψ0 = n0 and then consider small fluctuations around this state Ψ(r, t) = Ψ0 + δ Ψ(r, t). Linearized equations of motion are ˙ i δΨ ˙ −i δ Ψ∗ 1 2m 1 =− 2m =− 2 δ Ψ + U0 n0 (δ Ψ + δ Ψ∗ ) 2 δ Ψ∗ + U0 n0 (δ Ψ + δ Ψ∗ ) (3.36) 10CHAPTER 3. BOSE-EINSTEIN CONDENSATION OF WEAKLY INTERACTING ATOMIC GASE Keeping in mind representation of the instantaneous wavefunction Ψ(r, t) = n0 + δn(r, t) eiδφ(r,t) , it...
View Full Document

This document was uploaded on 02/27/2014 for the course PHYS 284 at Harvard.

Ask a homework question - tutors are online